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%%Page: 16 16
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%%Page: 19 19
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%%Page: 22 22
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%%Page: 30 30
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%%Page: 31 31
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%%Page: 32 32
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%%Page: 33 33
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%%Page: 34 34
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y Fk(0)903 2145 y Ft(in)g(\(5.15\))g(b)m(y)h(its)f(abbreviated)h
(expression)h(giv)m(en)f(in)e(\(5.8\).)43 b(Th)m(us)35
b(w)m(e)e(ha)m(v)m(e:)126 2293 y Fl(Z)209 2319 y Fn(t)173
2481 y Fm(0)288 2410 y Fq(O)363 2425 y Fm(3)402 2410
y Ft(\()p Fq(A)p Ft(\))g Fq(ds)116 b Ft(=)g Fq(h)1045
2425 y Fm(3)1085 2410 y Ft(\()p Fq(A)p Ft(\()p Fq(t)p
Ft(\))p Fq(;)17 b(t)p Ft(\))54 b Fp(\000)h Fq(h)1666
2425 y Fm(3)1706 2410 y Ft(\()p Fq(A)1817 2425 y Fm(0)1856
2410 y Fq(;)17 b Ft(0\))796 2646 y Fp(\000)966 2579 y
Ft(3)p Fq(\013)1077 2594 y Fm(30)p 966 2623 186 4 v 983
2714 a Ft(2)p Fq(i)p Ft(\012)1211 2529 y Fl(Z)1294 2555
y Fn(t)1257 2718 y Fm(0)1373 2646 y Fq(e)1418 2605 y
Fm(2)p Fn(i)p Fm(\012)p Fn(s)1565 2646 y Fq(A)1638 2605
y Fm(2)1727 2550 y Fl(h)1766 2646 y Fq(\013)1828 2661
y Fm(21)1935 2646 y Fp(j)p Fq(A)p Fp(j)2064 2605 y Fm(2)2103
2646 y Fq(A)55 b Ft(+)f Fq(O)2436 2661 y Fm(3)2475 2646
y Ft(\()p Fq(A)p Ft(\))h(+)g Fp(O)s Ft(\()p Fp(j)p Fq(A)p
Fp(j)3059 2605 y Fm(5)3098 2646 y Ft(\))f(+)h Fo(E)3427
2550 y Fl(i)3515 2646 y Fq(ds)797 2883 y Ft(+)974 2815
y Fq(\013)1036 2830 y Fm(12)p 966 2859 153 4 v 966 2951
a Ft(2)p Fq(i)p Ft(\012)1178 2765 y Fl(Z)1261 2792 y
Fn(t)1224 2954 y Fm(0)1340 2883 y Fq(e)1385 2841 y Fk(\000)p
Fm(2)p Fn(i)p Fm(\012)p Fn(s)p 1587 2805 74 4 v 1587
2883 a Fq(A)1660 2824 y Fm(2)1749 2786 y Fl(h)1788 2883
y Fq(\013)1850 2898 y Fm(21)1957 2883 y Fp(j)p Fq(A)p
Fp(j)2086 2841 y Fm(2)2125 2883 y Fq(A)g Ft(+)f Fq(O)2458
2898 y Fm(3)2497 2883 y Ft(\()p Fq(A)p Ft(\))h(+)f Fp(O)s
Ft(\()p Fp(j)p Fq(A)p Fp(j)3080 2841 y Fm(5)3119 2883
y Ft(\))h(+)g Fo(E)3449 2786 y Fl(i)3537 2883 y Fq(ds)797
3119 y Ft(+)974 3052 y Fq(\013)1036 3067 y Fm(12)p 966
3096 153 4 v 966 3187 a Ft(2)p Fq(i)p Ft(\012)1178 3002
y Fl(Z)1261 3028 y Fn(t)1224 3190 y Fm(0)1340 3119 y
Fq(e)1385 3078 y Fk(\000)p Fm(2)p Fn(i)p Fm(\012)p Fn(s)1619
3119 y Ft(2)p Fp(j)p Fq(A)p Fp(j)1797 3078 y Fm(2)1885
3023 y Fl(h)p 1924 3066 63 4 v 96 x Fq(\013)1987 3134
y Fm(21)2094 3119 y Fp(j)p Fq(A)p Fp(j)2223 3078 y Fm(2)p
2262 3041 74 4 v 2262 3119 a Fq(A)g Ft(+)p 2521 3041
78 4 v 55 w Fq(O)2598 3134 y Fm(3)2637 3119 y Ft(\()p
Fq(A)p Ft(\))g(+)f Fp(O)s Ft(\()p Fp(j)p Fq(A)p Fp(j)3220
3078 y Fm(5)3259 3119 y Ft(\))h(+)p 3483 3041 74 4 v
55 w Fo(E)3589 3023 y Fl(i)3677 3119 y Fq(ds)797 3355
y Ft(+)966 3288 y(3)p Fq(\013)1077 3303 y Fm(03)p 966
3332 186 4 v 983 3424 a Ft(4)p Fq(i)p Ft(\012)1211 3238
y Fl(Z)1294 3265 y Fn(t)1257 3427 y Fm(0)1373 3355 y
Fq(e)1418 3314 y Fk(\000)p Fm(4)p Fn(i)p Fm(\012)p Fn(s)p
1620 3277 74 4 v 1620 3355 a Fq(A)1693 3297 y Fm(2)1782
3259 y Fl(h)p 1821 3303 63 4 v 96 x Fq(\013)1884 3370
y Fm(21)1991 3355 y Fp(j)p Fq(A)p Fp(j)2120 3314 y Fm(2)p
2159 3277 74 4 v 2159 3355 a Fq(A)f Ft(+)p 2417 3277
78 4 v 55 w Fq(O)2494 3370 y Fm(3)2534 3355 y Ft(\()p
Fq(A)p Ft(\))g(+)h Fp(O)s Ft(\()p Fp(j)p Fq(A)p Fp(j)3117
3314 y Fm(5)3156 3355 y Ft(\))f(+)p 3379 3277 74 4 v
55 w Fo(E)3485 3259 y Fl(i)3573 3355 y Fq(ds)h Ft(\(5.17\))72
3604 y(Substitution)32 b(of)g(\(5.9\))g(in)m(to)g(\(5.17\))g(and)h(in)m
(tegrating)e(b)m(y)i(parts,)g(w)m(e)h(arriv)m(e)e(at)h(the)g(follo)m
(wing)d(expres-)-74 3754 y(sion:)403 3886 y Fl(Z)486
3912 y Fn(t)450 4074 y Fm(0)565 4003 y Fq(O)640 4018
y Fm(3)679 4003 y Ft(\()p Fq(A)p Ft(\))j Fq(ds)115 b
Ft(=)g Fq(h)1320 4018 y Fm(3)1360 4003 y Ft(\()p Fq(A)p
Ft(\()p Fq(t)p Ft(\))p Fq(;)17 b(t)p Ft(\))55 b(+)f Fq(h)1940
4018 y Fm(3)p Fn(a)2017 4003 y Ft(\()p Fq(A)p Ft(\()p
Fq(t)p Ft(\))p Fq(;)17 b(t)p Ft(\))55 b Fp(\000)22 b
Fq(h)2566 4018 y Fm(3)2606 4003 y Ft(\()p Fq(A)2717 4018
y Fm(0)2757 4003 y Fq(;)17 b Ft(0\))54 b Fp(\000)h Fq(h)3130
4018 y Fm(3)p Fn(a)3207 4003 y Ft(\()p Fq(A)3318 4018
y Fm(0)3357 4003 y Fq(;)17 b Ft(0\))1073 4239 y(+)1326
4172 y(1)p 1274 4216 153 4 v 1274 4308 a(2)p Fq(i)p Ft(\012)1486
4118 y Fl(\022)1557 4172 y Ft(3)p 1557 4216 49 4 v 1557
4308 a(2)1648 4239 y Fp(j)p Fq(\013)1738 4254 y Fm(03)1813
4239 y Fp(j)1841 4198 y Fm(2)1934 4239 y Fp(\000)56 b
Ft(2)p Fq(\013)2178 4254 y Fm(30)2252 4239 y Fq(\013)2314
4254 y Fm(12)2444 4239 y Ft(+)e(2)p Fp(j)p Fq(\013)2713
4254 y Fm(12)2787 4239 y Fp(j)2815 4198 y Fm(2)2854 4118
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Fm(0)3126 4239 y Fp(j)p Fq(A)p Fp(j)3255 4198 y Fm(4)3294
4239 y Fq(A)33 b(ds)1073 4479 y Ft(+)1264 4362 y Fl(Z)1347
4388 y Fn(t)1310 4551 y Fm(0)1426 4479 y Fp(O)1525 4383
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Fm(2)1742 4479 y Ft(\()p Fp(j)p Fq(A)p Fp(j)1909 4438
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4728 y(where)242 4977 y Fq(h)298 4992 y Fm(3)p Fn(a)375
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4925 y Fm(03)p 1073 4954 275 4 v 1131 5045 a Ft(2\012)1250
5017 y Fm(2)1413 4977 y Ft(+)1553 4910 y(3)p Fq(\013)1664
4925 y Fm(30)1739 4910 y Fq(\013)1801 4925 y Fm(21)p
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Ft(3)p Fq(\013)2690 4874 y Fm(2)2689 4934 y(30)p 2578
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4977 y Fq(A)2879 4936 y Fm(5)2951 4977 y Fq(e)2996 4936
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%%Page: 37 37
37 36 bop 719 91 a Ft(+)975 23 y(1)p 920 67 159 4 v 920
159 a(4\012)1039 130 y Fm(2)1138 -31 y Fl(\022)1231 91
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y Fm(12)1559 91 y Ft(+)1700 23 y(3)p 1700 67 49 4 v 1700
159 a(2)1759 91 y Fq(\013)1821 106 y Fm(03)p 1895 38
63 4 v 1895 91 a Fq(\013)1958 106 y Fm(12)2088 91 y Fp(\000)55
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106 y Fm(03)2597 91 y Ft(+)f(2)p Fq(\013)2838 106 y Fm(12)p
2913 38 V 2913 91 a Fq(\013)2975 106 y Fm(21)3050 -31
y Fl(\023)3160 91 y Fq(A)3233 50 y Fm(2)p 3273 13 74
4 v 3273 91 a Fq(A)3346 32 y Fm(3)3418 91 y Fq(e)3463
50 y Fk(\000)p Fm(2)p Fn(i)p Fm(\012)p Fn(t)719 330 y
Ft(+)975 263 y(1)p 920 307 159 4 v 920 399 a(8\012)1039
370 y Fm(2)1138 209 y Fl(\022)1231 330 y Fq(\013)1294
289 y Fm(2)1293 355 y(12)1423 330 y Ft(+)1563 263 y(3)p
1563 307 49 4 v 1563 399 a(2)1622 330 y Fq(\013)1684
345 y Fm(03)p 1759 277 63 4 v 1759 330 a Fq(\013)1821
345 y Fm(21)1951 330 y Ft(+)g(2)p Fq(\013)2192 345 y
Fm(12)p 2267 277 V 2267 330 a Fq(\013)2330 345 y Fm(30)2437
209 y Fl(\023)2580 330 y Fq(A)p 2653 252 74 4 v(A)2726
272 y Fm(4)2798 330 y Fq(e)2843 289 y Fk(\000)p Fm(4)p
Fn(i)p Fm(\012)p Fn(t)719 570 y Ft(+)975 502 y(1)p 920
546 159 4 v 920 638 a(4\012)1039 609 y Fm(2)1138 449
y Fl(\022)1241 502 y Ft(1)p 1241 546 49 4 v 1241 638
a(3)1300 570 y Fq(\013)1362 585 y Fm(03)1437 570 y Fq(\013)1499
585 y Fm(12)1628 570 y Ft(+)1769 502 y(1)p 1769 546 V
1769 638 a(2)1827 570 y Fq(\013)1889 585 y Fm(03)p 1964
517 63 4 v 1964 570 a Fq(\013)2027 585 y Fm(30)2134 449
y Fl(\023)p 2244 492 74 4 v 2244 570 a Fq(A)2317 511
y Fm(5)2389 570 y Fq(e)2434 529 y Fk(\000)p Fm(6)p Fn(i)p
Fm(\012)p Fn(t)2629 570 y Fq(:)1069 b Ft(\(5.19\))-74
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m(ust)f(no)m(w)g(obtain)e(an)-74 1056 y Fr(Exp)-5 b(ansion)34
b(of)508 985 y Fl(R)563 1011 y Fn(t)547 1081 y Fm(0)642
1056 y Fq(O)717 1071 y Fm(5)756 1056 y Ft(\()p Fq(A)p
Ft(\))f Fq(ds)p Ft(:)72 1251 y(F)-8 b(rom)31 b(\(5.10\))h(w)m(e)i(ha)m
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1386 y Fl(Z)941 1412 y Fn(t)904 1574 y Fm(0)1020 1503
y Fq(O)1095 1518 y Fm(5)1134 1503 y Ft(\()p Fq(A)p Ft(\))e
Fq(ds)115 b Ft(=)h Fq(h)1775 1518 y Fm(3)p Fn(b)1845
1503 y Ft(\()p Fq(A)p Ft(\()p Fq(t)p Ft(\))p Fq(;)17
b(t)p Ft(\))54 b Fp(\000)h Fq(h)2426 1518 y Fm(3)p Fn(b)2496
1503 y Ft(\()p Fq(A)2607 1518 y Fm(0)2647 1503 y Fq(;)17
b Ft(0\))1527 1739 y(+)1719 1622 y Fl(Z)1802 1648 y Fn(t)1765
1811 y Fm(0)1881 1739 y Fp(O)1979 1643 y Fl(\020)2061
1739 y Fp(j)p Fq(A)p Fp(j)2190 1698 y Fm(4)2229 1739
y Ft(\()p Fp(j)p Fq(A)p Fp(j)2396 1698 y Fm(3)2490 1739
y Ft(+)54 b Fp(j)p Fo(E)p Fp(j)p Ft(\))2820 1643 y Fl(\021)2918
1739 y Fq(ds;)683 b Ft(\(5.20\))-74 1975 y(where)494
2211 y Fq(h)550 2226 y Fm(3)p Fn(b)619 2211 y Ft(\()p
Fq(A;)17 b(t)p Ft(\))117 b(=)1174 2144 y Fq(\013)1236
2159 y Fm(50)p 1166 2188 153 4 v 1166 2279 a Ft(4)p Fq(i)p
Ft(\012)1361 2211 y Fq(A)1434 2170 y Fm(5)1506 2211 y
Fq(e)1551 2170 y Fm(4)p Fn(i)p Fm(\012)p Fn(t)1746 2211
y Ft(+)1894 2144 y Fq(\013)1956 2159 y Fm(41)p 1886 2188
V 1886 2279 a Ft(2)p Fq(i)p Ft(\012)2081 2211 y Fq(A)2154
2170 y Fm(4)p 2194 2133 74 4 v 2194 2211 a Fq(A)32 b(e)2344
2170 y Fm(2)p Fn(i)p Fm(\012)p Fn(t)2539 2211 y Fp(\000)2689
2144 y Fq(\013)2751 2159 y Fm(23)p 2681 2188 153 4 v
2681 2279 a Ft(2)p Fq(i)p Ft(\012)2876 2211 y Fq(A)2949
2170 y Fm(2)p 3021 2133 74 4 v 3021 2211 a Fq(A)3094
2153 y Fm(3)3166 2211 y Fq(e)3211 2170 y Fk(\000)p Fm(2)p
Fn(i)p Fm(\012)p Fn(t)963 2423 y Fp(\000)1174 2356 y
Fq(\013)1236 2371 y Fm(14)p 1166 2400 153 4 v 1166 2491
a Ft(4)p Fq(i)p Ft(\012)1361 2423 y Fq(A)p 1434 2345
74 4 v(A)1507 2365 y Fm(4)1579 2423 y Fq(e)1624 2382
y Fk(\000)p Fm(4)p Fn(i)p Fm(\012)p Fn(t)1874 2423 y
Fp(\000)2024 2356 y Fq(\013)2086 2371 y Fm(05)p 2016
2400 153 4 v 2016 2491 a Ft(6)p Fq(i)p Ft(\012)p 2211
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y Fq(e)2401 2382 y Fk(\000)p Fm(6)p Fn(i)p Fm(\012)p
Fn(t)2596 2423 y Fq(:)1102 b Ft(\(5.21\))-74 2659 y(Therefore)34
b(from)d(\(5.11\))h(and)h(our)f(computations)g(w)m(e)h(ha)m(v)m(e:)680
2895 y Fq(A)55 b Fp(\000)g Fq(h)996 2910 y Fm(3)1036
2895 y Ft(\()p Fq(A;)17 b(t)p Ft(\))54 b Fp(\000)h Fq(h)1506
2910 y Fm(3)p Fn(a)1583 2895 y Ft(\()p Fq(A;)17 b(t)p
Ft(\))55 b Fp(\000)g Fq(h)2054 2910 y Fm(3)p Fn(b)2124
2895 y Ft(\()p Fq(A;)17 b(t)p Ft(\))680 3069 y(=)60 b
Fq(A)889 3084 y Fm(0)983 3069 y Fp(\000)55 b Fq(h)1171
3084 y Fm(3)1211 3069 y Ft(\()p Fq(A)1322 3084 y Fm(0)1362
3069 y Fq(;)17 b Ft(0\))54 b Fp(\000)h Fq(h)1735 3084
y Fm(3)p Fn(a)1812 3069 y Ft(\()p Fq(A)1923 3084 y Fm(0)1962
3069 y Fq(;)17 b Ft(0\))54 b Fp(\000)h Fq(h)2335 3084
y Fm(3)p Fn(b)2405 3069 y Ft(\()p Fq(A)2516 3084 y Fm(0)2556
3069 y Fq(;)17 b Ft(0\))489 3259 y(+)647 3142 y Fl(Z)730
3168 y Fn(t)694 3331 y Fm(0)809 3259 y Fq(\013)871 3274
y Fm(21)979 3259 y Fp(j)p Fq(A)p Fp(j)1108 3218 y Fm(2)1146
3259 y Fq(A)55 b Ft(+)g Fq(\013)1467 3274 y Fm(32)1574
3259 y Fp(j)p Fq(A)p Fp(j)1703 3218 y Fm(4)1742 3259
y Fq(A)33 b(ds)489 3496 y Ft(+)742 3428 y(1)p 690 3472
153 4 v 690 3564 a(2)p Fq(i)p Ft(\012)902 3374 y Fl(\022)1005
3428 y Ft(3)p 1005 3472 49 4 v 1005 3564 a(2)1064 3496
y Fp(j)p Fq(\013)1154 3511 y Fm(03)1228 3496 y Fp(j)1256
3454 y Fm(2)1350 3496 y Fp(\000)55 b Ft(2)p Fq(\013)1593
3511 y Fm(30)1668 3496 y Fq(\013)1730 3511 y Fm(12)1859
3496 y Ft(+)g(2)p Fp(j)p Fq(\013)2129 3511 y Fm(12)2203
3496 y Fp(j)2231 3454 y Fm(2)2303 3374 y Fl(\023)2413
3378 y(Z)2496 3405 y Fn(t)2459 3567 y Fm(0)2575 3496
y Fp(j)p Fq(A)p Fp(j)2704 3454 y Fm(4)2742 3496 y Fq(A)33
b(ds)54 b Ft(+)3130 3378 y Fl(Z)3213 3405 y Fn(t)3176
3567 y Fm(0)3292 3496 y Fo(E)32 b Fq(ds)489 3735 y Ft(+)680
3618 y Fl(Z)763 3644 y Fn(t)726 3807 y Fm(0)842 3735
y Fp(O)940 3639 y Fl(\020)1023 3735 y Fp(j)p Fq(A)p Fp(j)1152
3694 y Fm(4)1190 3735 y Ft(\()p Fp(j)p Fq(A)p Fp(j)1357
3694 y Fm(3)1451 3735 y Ft(+)22 b Fp(j)p Fo(E)p Fp(j)p
Ft(\))1748 3639 y Fl(\021)1853 3735 y Ft(+)54 b Fp(O)2082
3639 y Fl(\020)2164 3735 y Fp(j)p Fq(A)p Fp(j)2293 3694
y Fm(2)2332 3735 y Ft(\()p Fp(j)p Fq(A)p Fp(j)2499 3694
y Fm(5)2592 3735 y Ft(+)22 b Fp(j)p Fo(E)p Fp(j)p Ft(\))2890
3639 y Fl(\021)2988 3735 y Fq(ds:)613 b Ft(\(5.22\))72
3971 y(This)33 b(suggests)h(the)f(c)m(hange)h(of)e(v)-5
b(ariables:)1139 4207 y Fq(A)1212 4222 y Fm(1)1368 4207
y Fp(\021)116 b Fq(A)54 b Fp(\000)h Fq(H)1901 4222 y
Fm(1)1941 4207 y Ft(\()p Fq(A;)17 b(t)p Ft(\))p Fq(;)114
b Ft(where)904 4382 y Fq(H)985 4397 y Fm(1)1024 4382
y Ft(\()p Fq(A;)17 b(t)p Ft(\))116 b(=)h Fq(h)1617 4397
y Fm(3)1656 4382 y Ft(\()p Fq(A;)17 b(t)p Ft(\))55 b(+)f
Fq(h)2125 4397 y Fm(3)p Fn(a)2202 4382 y Ft(\()p Fq(A;)17
b(t)p Ft(\))55 b(+)f Fq(h)2671 4397 y Fm(3)p Fn(b)2741
4382 y Ft(\()p Fq(A;)17 b(t)p Ft(\))p Fq(;)729 b Ft(\(5.23\))-74
4618 y(whic)m(h)41 b(for)e(small)f Fp(j)p Fq(A)p Fp(j)p
Ft(,)k(is)d(a)h(near-iden)m(tit)m(y)g(c)m(hange)h(of)f(v)-5
b(ariables.)65 b(Using)39 b(this)h(c)m(hange)h(of)f(v)-5
b(ariables)39 b(w)m(e)-74 4767 y(ha)m(v)m(e)34 b(that)e(\(5.22\))g(b)s
(ecomes)417 5019 y Fq(A)490 5034 y Fm(1)645 5019 y Ft(=)115
b Fq(A)909 5034 y Fm(10)1039 5019 y Ft(+)1169 4901 y
Fl(Z)1252 4928 y Fn(t)1215 5090 y Fm(0)1331 5019 y Fq(\013)1393
5034 y Fm(21)1500 5019 y Fp(j)p Fq(A)1601 5034 y Fm(1)1641
5019 y Fp(j)1669 4977 y Fm(2)1708 5019 y Fq(A)1781 5034
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5019 y Fp(j)p Fq(A)2276 5034 y Fm(1)2315 5019 y Fp(j)2343
4977 y Fm(4)2382 5019 y Fq(A)2455 5034 y Fm(1)2527 5019
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%%Page: 38 38
38 37 bop 645 91 a Ft(+)898 23 y(1)p 846 68 153 4 v 846
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%%Page: 39 39
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y Fm(0)1080 5057 y Fp(j)1108 5021 y Fm(4)1147 5057 y
Fp(g)p Fi(.)1901 5306 y Ft(39)p eop
%%Page: 40 40
40 39 bop -74 59 a Fr(pr)-5 b(o)g(of:)43 b Ft(Use)33
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Ft(and)33 b Fq(q)e Ft(=)1030 4859 y Fm(8)p 1030 4875
V 1030 4933 a(5)1075 4898 y Ft(.)1901 5306 y(40)p eop
%%Page: 41 41
41 40 bop 72 59 a Ft(This)33 b(last)f(estimate)g(can)h(no)m(w)g(b)s(e)g
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b(z)2200 650 y Fm(0)2239 635 y Fq(;)82 b Ft(is)661 874
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2078 851 487 4 v 2078 957 a Fq(\015)2144 893 y Fj(3)p
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y Fq(m)2621 1413 y Fk(\003)p 2273 1442 487 4 v 2273 1548
a Fq(\015)2339 1485 y Fj(3)p 2339 1497 31 4 v 2339 1538
a(5)2383 1548 y Fq(z)2428 1563 y Fm(0)2468 1548 y Fp(h)p
Fq(t)p Fp(i)2581 1512 y Fm(1+)2681 1485 y Fj(8)p 2681
1497 V 2681 1538 a(5)2721 1512 y Fn(\016)2769 1466 y
Fq(:)929 b Ft(\(6.17\))72 1742 y(Multiplication)29 b(b)m(y)34
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2062 y Fm(0)1335 2047 y Fq(\015)5 b(t)p Ft(\))33 b Fq(S)6
b Ft(\()p Fq(t)p Ft(\))32 b(])116 b Fp(\024)g Fq(C)2129
1980 y(Q)2216 1893 y Fj(8)p 2216 1905 V 2216 1946 a(5)2206
2002 y Fm(0)2293 1980 y Fq(m)2378 1995 y Fk(\003)p 2129
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2078 31 4 v 2242 2119 a(5)2286 2130 y Fq(z)2331 2145
y Fm(0)2470 1980 y Ft(1)22 b(+)g(4)33 b Fq(z)2766 1995
y Fm(0)2805 1980 y Fq(\015)5 b(t)p 2470 2024 427 4 v
2544 2116 a Ft(\(1)21 b(+)h Fq(t)p Ft(\))3025 1980 y(1)p
2949 2024 201 4 v 2949 2130 a Fp(h)p Fq(t)p Fp(i)3072
2066 y Fj(8)p 3072 2078 31 4 v 3072 2119 a(5)3112 2093
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2352 290 4 v 2176 2458 a Fq(\015)2242 2394 y Fj(3)p 2242
2406 31 4 v 2242 2447 a(5)2286 2458 y Fq(z)2331 2473
y Fm(0)2547 2308 y Ft(1)p 2470 2352 201 4 v 2470 2458
a Fp(h)p Fq(t)p Fp(i)2593 2394 y Fj(8)p 2593 2406 31
4 v 2593 2447 a(5)2634 2421 y Fn(\016)2681 2375 y Fq(:)1017
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Fq(t)p Ft(\))60 b Fp(\024)h Fq(C)1907 2934 y(Q)1994 2847
y Fj(8)p 1995 2859 V 1995 2900 a(5)1984 2956 y Fm(0)2072
2934 y Fq(m)2157 2898 y Fm(2)2157 2959 y Fk(\003)p 1907
2978 290 4 v 1954 3084 a Fq(\015)2020 3020 y Fj(3)p 2020
3032 31 4 v 2020 3074 a(5)2065 3084 y Fq(z)2110 3099
y Fm(0)2325 2934 y Ft(1)p 2249 2978 201 4 v 2249 3084
a Fp(h)p Fq(t)p Fp(i)2372 3020 y Fj(8)p 2372 3032 31
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b Ft(\(6.19\))-74 3243 y(The)34 b(Lemma)d(no)m(w)i(follo)m(ws)e(from)h
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Fq(B)5 b(\021)1380 571 y Fm(3)1455 556 y Ft(is)36 b(driv)m(en)h(b)m(y)g
(terms)f(whic)m(h)h(are)f(formally)d(of)j(order)g Fp(h)p
Fq(t)p Fp(i)3596 520 y Fk(\000)p Fm(1)3690 556 y Ft(.)54
b(Esti-)-74 706 y(mation)37 b(in)h Fq(L)449 669 y Fm(4)528
706 y Ft(will)e(lead)i(to)h(con)m(v)m(olution)f(of)g
Fp(h)p Fq(t)p Fp(i)1815 669 y Fk(\000)p Fm(1)1948 706
y Ft(with)h Fp(h)p Fq(t)p Fp(i)2290 669 y Fk(\000)p Fm(1)p
Fn(=)p Fm(2)2493 706 y Ft(giving)e(a)i(rate)g(of)f Fp(h)p
Fq(t)p Fp(i)3314 669 y Fk(\000)p Fm(1)p Fn(=)p Fm(2+)p
Fn(\016)3560 678 y Fj(0)3599 706 y Ft(,)j(for)d(an)m(y)-74
855 y Fq(\016)-31 870 y Fm(0)36 855 y Fq(>)28 b Ft(0.)72
1104 y(F)-8 b(or)32 b(0)c Fp(\024)g Fq(t)g Fp(\024)g
Fq(T)14 b Ft(,)32 b(with)g Fq(T)47 b Ft(\014xed)33 b(and)g(arbitrary)-8
b(,)32 b(w)m(e)h(ha)m(v)m(e:)559 1502 y Fp(j)p Fq(A)p
Fp(j)688 1461 y Fm(2)760 1502 y Fp(jj)p Fq(')880 1461
y Fm(2)919 1502 y Fq(\021)t Fp(jj)1027 1517 y Fm(4)p
Fn(=)p Fm(3)p Fn(;)p Fm(1)1306 1502 y Fp(\024)116 b Fq(C)1569
1517 y Fn(')1652 1502 y Ft([)p Fq(A)p Ft(])1779 1461
y Fm(2)1779 1527 y(1)p Fn(=)p Fm(4)1938 1406 y Fl(\020)1988
1502 y Ft([)p Fq(\021)t Ft(])2094 1517 y Fm(8)p Fn(;)p
Fm(3)p Fn(=)p Fm(4)2258 1502 y Fp(h)p Fq(t)p Fp(i)2371
1461 y Fk(\000)p Fm(5)p Fn(=)p Fm(4)2591 1502 y Ft(+)54
b([)p Fq(B)5 b(\021)2875 1517 y Fm(1)2915 1502 y Ft(])2942
1517 y Fm(4)p Fn(;)p Fm(1)p Fn(=)p Fm(2)3107 1502 y Fp(h)p
Fq(t)p Fp(i)3220 1461 y Fk(\000)p Fm(1)1307 1685 y Ft(+)126
b([)p Fq(B)5 b(\021)1663 1700 y Fm(2)1703 1685 y Ft(])1730
1700 y Fm(4)p Fn(;)p Fm(1)p Fn(=)p Fm(2)1895 1685 y Fp(h)p
Fq(t)p Fp(i)2008 1644 y Fk(\000)p Fm(1)2157 1685 y Ft(+)54
b([)p Fq(B)5 b(\021)2441 1700 y Fm(3)2481 1685 y Ft(])2508
1700 y Fm(4)p Fn(;)p Fm(1)p Fn(=)p Fm(2)p Fk(\000)p Fn(\016)2754
1709 y Fj(0)2794 1685 y Fp(h)p Fq(t)p Fp(i)2907 1644
y Fk(\000)p Fm(1+)p Fn(\016)3083 1653 y Fj(0)3121 1588
y Fl(\021)3187 1685 y Fq(;)-74 1933 y Ft(where)34 b Fq(\016)251
1948 y Fm(0)323 1933 y Ft(is)e(p)s(ositiv)m(e)g(and)h(arbitrary)-8
b(.)42 b(Also,)459 2182 y Fp(j)p Fq(A)p Fp(j)32 b(jj)p
Fq('\021)792 2141 y Fm(2)831 2182 y Fp(jj)887 2198 y
Fm(1)p Fn(;)p Fm(4)p Fn(=)p Fm(3)1166 2182 y Fp(\024)84
b Fq(C)1397 2197 y Fn(')1479 2182 y Ft([)p Fq(A)p Ft(])1606
2198 y Fm(1)p Fn(=)p Fm(4)1733 2086 y Fl(\020)1815 2182
y Ft([)p Fq(\021)t Ft(])1921 2141 y Fm(2)1921 2207 y(8)p
Fn(;)p Fm(3)p Fn(=)p Fm(4)2086 2182 y Fp(h)p Fq(t)p Fp(i)2199
2141 y Fk(\000)p Fm(7)p Fn(=)p Fm(4)2418 2182 y Ft(+)55
b([)p Fq(\021)t Ft(])2655 2198 y Fm(8)p Fn(;)p Fm(3)p
Fn(=)p Fm(4)2820 2182 y Ft([)p Fq(B)5 b(\021)2974 2197
y Fm(1)3014 2182 y Ft(])3041 2197 y Fm(4)p Fn(;)p Fm(0)3135
2182 y Fp(h)p Fq(t)p Fp(i)3248 2141 y Fk(\000)p Fm(1)3375
2086 y Fl(\021)684 2356 y Fp(jj)p Fq(\021)792 2315 y
Fm(3)831 2356 y Fp(jj)887 2372 y Fm(1)p Fn(;)p Fm(4)p
Fn(=)p Fm(3)1166 2356 y Fp(\024)116 b(jj)p Fq(\021)t
Fp(jj)1523 2371 y Fm(1)p Fn(;)p Fm(2)1649 2356 y Ft([)p
Fq(\021)t Ft(])1755 2315 y Fm(2)1755 2381 y(8)p Fn(;)p
Fm(3)p Fn(=)p Fm(4)1952 2356 y Fp(h)p Fq(t)p Fp(i)2065
2315 y Fk(\000)p Fm(3)p Fn(=)p Fm(2)2230 2356 y Fq(:)-74
2605 y Ft(It)33 b(follo)m(ws)e(that)h(for)g(0)c Fp(\024)g
Fq(t)g Fp(\024)g Fq(T)783 2854 y Fp(jj)p Fq(B)5 b(\021)966
2869 y Fm(3)1005 2854 y Fp(jj)1061 2869 y Fm(4)1160 2854
y Fp(\024)61 b Fq(C)1368 2869 y Fn(')1418 2854 y Fp(j)p
Fq(\025)p Fp(j)1579 2737 y Fl(Z)1662 2763 y Fn(t)1625
2925 y Fm(0)1741 2854 y Fp(j)p Fq(t)22 b Fp(\000)h Fq(s)p
Fp(j)2000 2813 y Fk(\000)p Fm(1)p Fn(=)p Fm(2)2197 2854
y Fq(ds)p Fp(h)p Fq(t)p Fp(i)2407 2813 y Fk(\000)p Fm(1+)p
Fn(\016)2583 2822 y Fj(0)2654 2854 y Fq(G)p Ft(\()p Fq(A;)17
b(\021)t(;)g(T)d Ft(\))p Fq(;)607 b Ft(\(7.39\))-74 3103
y(where)292 3351 y Fq(G)p Ft(\()p Fq(A;)17 b(\021)t(;)g(T)d
Ft(\))114 b Fp(\021)i Ft([)p Fq(A)p Ft(])1163 3310 y
Fm(2)1163 3376 y(1)p Fn(=)p Fm(4)1323 3255 y Fl(\020)1405
3351 y Ft([)p Fq(\021)t Ft(])1511 3367 y Fm(8)p Fn(;)p
Fm(3)p Fn(=)p Fm(4)1730 3351 y Ft(+)55 b([)p Fq(B)5 b(\021)2015
3366 y Fm(1)2055 3351 y Ft(])2082 3367 y Fm(4)p Fn(;)p
Fm(1)p Fn(=)p Fm(2)2301 3351 y Ft(+)55 b([)p Fq(B)5 b(\021)2586
3366 y Fm(2)2626 3351 y Ft(])2653 3367 y Fm(4)p Fn(;)p
Fm(1)p Fn(=)p Fm(2)2872 3351 y Ft(+)55 b([)p Fq(B)5 b(\021)3157
3366 y Fm(3)3197 3351 y Ft(])3224 3367 y Fm(4)p Fn(;)p
Fm(1)p Fn(=)p Fm(2)p Fk(\000)p Fn(\016)3470 3376 y Fj(0)3542
3255 y Fl(\021)844 3534 y Ft(+)84 b([)p Fq(A)p Ft(])1131
3549 y Fm(1)p Fn(=)p Fm(4)1290 3438 y Fl(\020)1372 3534
y Ft([)p Fq(\021)t Ft(])1478 3493 y Fm(2)1478 3559 y(8)p
Fn(;)p Fm(3)p Fn(=)p Fm(4)1698 3534 y Ft(+)54 b([)p Fq(\021)t
Ft(])1934 3549 y Fm(8)p Fn(;)p Fm(3)p Fn(=)p Fm(4)2132
3534 y Ft([)p Fq(B)5 b(\021)2286 3549 y Fm(1)2325 3534
y Ft(])2352 3549 y Fm(4)p Fn(;)p Fm(0)2479 3438 y Fl(\021)2584
3534 y Ft(+)22 b Fp(jj)p Fq(\021)t Fp(jj)2846 3549 y
Fm(1)p Fn(;)p Fm(2)2971 3534 y Ft([)p Fq(\021)t Ft(])3077
3493 y Fm(2)3077 3559 y(8)p Fn(;)p Fm(3)p Fn(=)p Fm(4)3242
3534 y Fq(:)72 3783 y Ft(Therefore,)34 b(for)e(0)c Fp(\024)g
Fq(t)g Fp(\024)g Fq(T)14 b Ft(:)1042 4031 y Fp(jj)p Fq(B)5
b(\021)1225 4046 y Fm(3)1264 4031 y Ft(\()p Fq(t)p Ft(\))p
Fp(jj)1431 4046 y Fm(4)1530 4031 y Fp(\024)60 b Fq(C)1737
4046 y Fn(')1787 4031 y Fp(j)p Fq(\025)p Fp(j)32 b Fq(G)p
Ft(\()p Fq(A;)17 b(\021)t(;)g(T)d Ft(\))31 b Fp(h)p Fq(t)p
Fp(i)2513 3990 y Fk(\000)p Fm(1)p Fn(=)p Fm(2+)p Fn(\016)2759
3999 y Fj(0)2799 4031 y Fq(;)899 b Ft(\(7.40\))-74 4280
y(for)28 b(an)m(y)g Fq(\016)293 4295 y Fm(0)361 4280
y Fq(>)f Ft(0.)42 b(W)-8 b(e)28 b(no)m(w)h(use)g(the)f(estimate)f
(\(7.40\))h(in)f(\(7.22\))g(in)g(order)i(to)e(obtain)g(a)h(b)s(ound)g
(on)g Fp(jj)p Fq(\021)3702 4295 y Fm(3)3741 4280 y Ft(\()p
Fq(t)p Ft(\))p Fp(jj)3908 4295 y Fm(8)3947 4280 y Ft(.)-74
4430 y(First,)k(a)g(consequence)k(of)c(\(7.22\),)g(\(7.33\),)g
(\(7.35\))f(and)i(\(7.40\))f(is)g(that)g(for)g(0)c Fp(\024)g
Fq(t)g Fp(\024)g Fq(T)14 b Ft(:)-74 4678 y Fp(j)p Fq(A)p
Fp(j)55 4637 y Fm(2)127 4678 y Fp(jj)p Fq(')247 4637
y Fm(2)285 4678 y Fq(\021)t Fp(jj)393 4694 y Fm(1)p Fn(;)p
Fm(8)p Fn(=)p Fm(7)673 4678 y Fp(\024)116 b Fq(C)936
4693 y Fn(')1018 4678 y Ft([)p Fq(A)p Ft(])1145 4637
y Fm(2)1145 4703 y(1)p Fn(=)p Fm(4)1305 4582 y Fl(\020)1387
4678 y Ft([)p Fq(\021)t Ft(])1493 4694 y Fm(8)p Fn(;)p
Fm(3)p Fn(=)p Fm(4)1712 4678 y Ft(+)55 b Fp(k)p Fo(u)1955
4693 y Fm(0)1994 4678 y Fp(k)2044 4693 y Fh(X)2164 4678
y Ft(+)g([)p Fq(A)p Ft(])2422 4637 y Fm(3)2422 4703 y(1)p
Fn(=)p Fm(4)2587 4678 y Ft(+)f([)p Fq(B)5 b(\021)2871
4693 y Fm(3)2911 4678 y Ft(])2938 4694 y Fm(4)p Fn(;)p
Fm(1)p Fn(=)p Fm(2)p Fk(\000)p Fn(\016)3184 4703 y Fj(0)3256
4582 y Fl(\021)3355 4678 y Fp(h)p Fq(t)p Fp(i)3468 4637
y Fk(\000)p Fm(1+)p Fn(\016)3644 4646 y Fj(0)3683 4678
y Fq(;)-34 4861 y Fp(j)p Fq(A)p Fp(j)32 b(jj)p Fq('\021)299
4820 y Fm(2)337 4861 y Fp(jj)393 4876 y Fm(1)p Fn(;)p
Fm(8)p Fn(=)p Fm(7)673 4861 y Fp(\024)116 b Fq(C)936
4876 y Fn(')1018 4861 y Ft([)p Fq(A)p Ft(])1145 4876
y Fm(1)p Fn(=)p Fm(4)1305 4765 y Fl(\020)1387 4861 y
Ft([)p Fq(\021)t Ft(])1493 4820 y Fm(2)1493 4886 y(8)p
Fn(;)p Fm(3)p Fn(=)p Fm(4)1712 4861 y Ft(+)55 b Fp(fk)p
Fo(u)2005 4876 y Fm(0)2044 4861 y Fp(k)2094 4876 y Fh(X)2214
4861 y Ft(+)f([)p Fq(B)5 b(\021)2498 4876 y Fm(3)2538
4861 y Ft(])2565 4876 y Fm(4)p Fn(;)p Fm(1)p Fn(=)p Fm(2)p
Fk(\000)p Fn(\016)2811 4885 y Fj(0)2906 4861 y Ft(+)54
b([)p Fq(A)p Ft(])3163 4820 y Fm(3)3163 4886 y(1)p Fn(=)p
Fm(4)3273 4861 y Fp(g)33 b Ft([)p Fq(\021)t Ft(])3462
4876 y Fm(8)p Fn(;)p Fm(3)p Fn(=)p Fm(4)3659 4765 y Fl(\021)3758
4861 y Fp(h)p Fq(t)p Fp(i)3871 4820 y Fk(\000)p Fm(1+)p
Fn(\016)4047 4829 y Fj(0)4086 4861 y Fq(;)190 5045 y
Fp(jj)p Fq(\021)298 5003 y Fm(3)337 5045 y Fp(jj)393
5060 y Fm(1)p Fn(;)p Fm(8)p Fn(=)p Fm(7)673 5045 y Fp(\024)116
b Fq(C)936 5060 y Fn(')1002 5045 y Ft(\()p Fp(jj)p Fq(\021)t
Fp(jj)1204 5060 y Fm(1)p Fn(;)p Fm(2)1297 5045 y Ft(\))49
b([)p Fq(\021)t Ft(])1490 4994 y Fm(5)p Fn(=)p Fm(3)1490
5073 y(8)p Fn(;)p Fm(3)p Fn(=)p Fm(4)1687 5045 y Fp(h)p
Fq(t)p Fp(i)1800 5003 y Fk(\000)p Fm(5)p Fn(=)p Fm(4)1965
5045 y Fq(:)1888 b Ft(\(7.41\))1901 5306 y(47)p eop
%%Page: 48 48
48 47 bop -74 59 a Ft(Substitution)32 b(of)g(\(7.41\))g(in)m(to)g
(\(7.17-7.20\))e(leads)j(to)f(an)g(estimate)g(for)g Fp(jj)p
Fq(\021)2706 74 y Fm(3)2745 59 y Ft(\()p Fq(t)p Ft(\))p
Fp(jj)2912 74 y Fm(8)2951 59 y Ft(.)43 b(F)-8 b(or)32
b(0)c Fp(\024)g Fq(t)g Fp(\024)g Fq(T)14 b Ft(:)181 308
y Fp(jj)p Fq(\021)285 323 y Fm(3)324 308 y Ft(\()p Fq(t)p
Ft(\))p Fp(jj)491 323 y Fm(8)646 308 y Fp(\024)116 b(j)p
Fq(\025)p Fp(j)31 b Fq(C)1053 323 y Fn(')1136 308 y Fp(h)p
Fq(t)p Fp(i)1249 267 y Fk(\000)p Fm(1+)p Fn(\016)1425
276 y Fj(0)1513 308 y Ft(\()26 b([)p Fq(A)p Ft(])1704
267 y Fm(2)1704 332 y(1)p Fn(=)p Fm(4)1815 308 y Fp(f)p
Ft([)p Fq(\021)t Ft(])1971 323 y Fm(8)p Fn(;)p Fm(3)p
Fn(=)p Fm(4)2190 308 y Ft(+)54 b Fp(k)p Fo(u)2432 323
y Fm(0)2472 308 y Fp(k)2522 323 y Fh(X)2609 308 y Ft(+)h([)p
Fq(A)p Ft(])2867 267 y Fm(3)2867 332 y(1)p Fn(=)p Fm(4)3032
308 y Ft(+)f([)p Fq(B)5 b(\021)3316 323 y Fm(3)3356 308
y Ft(])3383 323 y Fm(4)p Fn(;)p Fm(1)p Fn(=)p Fm(2)p
Fk(\000)p Fn(\016)3629 332 y Fj(0)3669 308 y Fp(g)647
482 y Ft(+)83 b([)p Fq(A)p Ft(])933 498 y Fm(1)p Fn(=)p
Fm(4)1076 482 y Fp(f)32 b Ft([)p Fq(\021)t Ft(])1264
441 y Fm(2)1264 507 y(8)p Fn(;)p Fm(3)p Fn(=)p Fm(4)1484
482 y Ft(+)1614 386 y Fl(h)1686 482 y Fp(k)p Fo(u)1798
497 y Fm(0)1838 482 y Fp(k)1888 497 y Fh(X)1975 482 y
Ft(+)54 b([)p Fq(B)5 b(\021)2259 497 y Fm(3)2299 482
y Ft(])2326 498 y Fm(4)p Fn(;)p Fm(1)p Fn(=)p Fm(2)p
Fk(\000)p Fn(\016)2572 507 y Fj(0)2667 482 y Ft(+)54
b([)p Fq(A)p Ft(])2924 441 y Fm(3)2924 507 y(1)p Fn(=)p
Fm(4)3067 386 y Fl(i)3155 482 y Ft([)p Fq(\021)t Ft(])3261
498 y Fm(8)p Fn(;)p Fm(3)p Fn(=)p Fm(4)3459 482 y Fp(g)647
666 y Ft(+)116 b Fq(C)23 b Ft(\()p Fp(jj)p Fq(\021)t
Fp(jj)1134 681 y Fm(1)p Fn(;)p Fm(2)1227 666 y Fq(;)17
b(')p Ft(\))49 b([)p Fq(\021)t Ft(])1528 615 y Fm(5)p
Fn(=)p Fm(3)1528 695 y(8)p Fn(;)p Fm(3)p Fn(=)p Fm(4)1751
666 y Ft(\))17 b Fq(;)1892 b Ft(\(7.42\))-74 915 y(where)34
b Fq(\016)251 930 y Fm(0)323 915 y Ft(is)e(arbitary)-8
b(.)72 1064 y(Finally)30 b(w)m(e)k(can)f(no)m(w)g(estimate)f
Fq(F)1384 1079 y Fm(2)1423 1064 y Ft(\()p Fq(a;)17 b(\021)1604
1079 y Fm(3)1644 1064 y Ft(\))32 b(using)g(\(4.18\))g(and)h(\(7.42\).)
43 b(Cho)s(osing)32 b Fq(\016)3230 1079 y Fm(0)3302 1064
y Ft(so)h(that)1167 1313 y Fp(\000)p Ft(1)22 b(+)g Fq(\016)1456
1328 y Fm(0)1556 1313 y Ft(=)60 b Fp(\000)p Ft(3)p Fq(=)p
Ft(4)22 b Fp(\000)h Fq(\033)2093 1328 y Fm(0)2133 1313
y Fq(;)49 b Ft(with)32 b Fq(\033)2486 1328 y Fm(0)2554
1313 y Fq(>)27 b Ft(0)p Fq(;)-74 1562 y Ft(w)m(e)34 b(ha)m(v)m(e)-74
1795 y Fo(Prop)s(osition)i(7.4.)128 2044 y Fp(j)p Fq(F)219
2059 y Fm(2)259 2044 y Ft(\()p Fq(a;)17 b(\021)440 2059
y Fm(3)479 2044 y Ft(\))p Fp(j)148 b(\024)116 b Fq(C)956
2059 y Fn(')1006 2044 y Fp(j)p Fq(\025)p Fp(j)32 b Ft([)p
Fq(A)p Ft(])1278 2003 y Fm(2)1278 2069 y(1)p Fn(=)p Fm(4)1437
1948 y Fl(\020)1519 2044 y Ft([)p Fq(A)p Ft(])1646 2003
y Fm(2)1646 2069 y(1)p Fn(=)p Fm(4)1756 2044 y Fp(f)h
Ft([)p Fq(\021)t Ft(])1945 2060 y Fm(8)p Fn(;)p Fm(3)p
Fn(=)p Fm(4)2164 2044 y Ft(+)55 b Fp(k)p Fo(u)2407 2059
y Fm(0)2446 2044 y Fp(j)2474 2059 y Fh(X)2594 2044 y
Ft(+)g([)p Fq(A)p Ft(])2852 2003 y Fm(3)2852 2069 y(1)p
Fn(=)p Fm(4)3016 2044 y Ft(+)g([)p Fq(B)5 b(\021)3301
2059 y Fm(3)3341 2044 y Ft(])3368 2060 y Fm(4)p Fn(;)p
Fm(1)p Fn(=)p Fm(4+)p Fn(\033)3623 2069 y Fj(0)3695 2044
y Fp(g)694 2227 y Ft(+)83 b([)p Fq(A)p Ft(])980 2242
y Fm(1)p Fn(=)p Fm(4)1123 2227 y Fp(f)33 b Ft([)p Fq(\021)t
Ft(])1312 2186 y Fm(2)1312 2251 y(8)p Fn(;)p Fm(3)p Fn(=)p
Fm(4)1531 2227 y Ft(+)1661 2130 y Fl(h)1701 2227 y Fp(k)p
Fo(u)1813 2242 y Fm(0)1852 2227 y Fp(k)1902 2242 y Fh(X)2022
2227 y Ft(+)55 b([)p Fq(A)p Ft(])2280 2186 y Fm(3)2280
2251 y(1)p Fn(=)p Fm(4)2445 2227 y Ft(+)f([)p Fq(B)5
b(\021)2729 2242 y Fm(3)2769 2227 y Ft(])2796 2242 y
Fm(4)p Fn(;)p Fm(1)p Fn(=)p Fm(4+)p Fn(\033)3051 2251
y Fj(0)3123 2130 y Fl(i)3212 2227 y Ft([)p Fq(\021)t
Ft(])3318 2242 y Fm(8)p Fn(;)p Fm(3)p Fn(=)p Fm(4)3482
2227 y Fp(g)694 2410 y Ft(+)158 b Fq(C)24 b Ft(\()p Fp(jj)p
Fq(\021)t Fp(jj)1224 2425 y Fm(1)p Fn(;)p Fm(2)1317 2410
y Fq(;)17 b(')p Ft(\))48 b([)p Fq(\021)t Ft(])1617 2359
y Fm(5)p Fn(=)p Fm(3)1617 2439 y(8)p Fn(;)p Fm(3)p Fn(=)p
Fm(4)1815 2314 y Fl(\021)1913 2410 y Fp(h)p Fq(t)p Fp(i)2026
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p Ft(.)-74 1603 y Fo(2.)50 b(Disp)s(ersiv)m(e)37 b(Hamiltonian)d
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Fq(A)825 2010 y Fk(0)877 2051 y Ft(=)c Fq(i)1030 1955
y Fl(\020)1080 2051 y Fq(c)1122 2066 y Fm(10)1218 2051
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y Fm(4)2028 2051 y Ft(+)g Fq(:::)g Ft(+)g Fq(c)2369 2066
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b(Hamiltonian)i(normal)-74 2404 y(form)760 2553 y Fq(A)833
2512 y Fk(0)884 2553 y Ft(=)988 2457 y Fl(\020)1037 2553
y Fq(k)1088 2568 y Fm(10)1185 2553 y Ft(+)22 b Fq(k)1334
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Fb(\003)3394 4006 y Ft(,)h(whic)m(h)f(w)m(ould)-74 4156
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y Fj(1)p 2753 4544 105 4 v 2753 4585 a(2)p Fg(n)2821
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5067 y Fn(n)p Fm(+1)p Fn(;n)3610 5052 y Ft(are)e(zero.)1901
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53 52 bop -74 59 a Ft(Do)s(es)30 b(the)g(v)-5 b(anishing)29
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208 y(time-in)m(v)-5 b(arian)m(ts)30 b(for)i(the)h(in)m(tegrable)f
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h(systems?)-74 656 y(Our)23 b(analysis)g(and)g(the)g(ab)s(o)m(v)m(e)h
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1254 y Fo(4.)48 b(Relation)29 b(to)i(cen)m(ter)g(manifold)f(theory:)41
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b(conserv)-5 b(a-)-74 1404 y(tiv)m(e)25 b(dynamical)e(system)j(in)m(to)
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b(There,)37 b(it)d(is)h(often)g(p)s(ossible)g(using)g(the)g(cen)m(ter)i
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1852 y(in)m(v)-5 b(arian)m(t)34 b(cen)m(ter-stable)i(manifold.)48
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3795 y Fo(5.)104 b(Systems)56 b(with)e(disorder:)75 b
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4392 y(Related)32 b(questions)i(are)e(studied)h(in)f([22],)g([25],)h
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54 53 bop -74 59 a Fs(References)-25 307 y Ft([1])49
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456 y(Bounds)40 b(on)g(Eigenfunctions)f(of)g(N-Bo)s(dy)h(Sc)m(hr\177)
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56 55 bop -74 59 a Ft([27])49 b(C.)40 b(G)m(\023)-46
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57 56 bop -74 59 a Ft([41])49 b(D.W.)26 b(McLaughlin)f(&)h(A.C.)h
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1055 y([44])49 b(F.)f(Nier,)53 b Fr(The)c(dynamics)g(of)h(some)f(op)-5
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4260 y(Mathematical)e(Sciences)k Fo(59)f Ft(Springer-V)-8
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4874 y([54])49 b(H.)30 b(Segur)g(&)f(M.D.)h(Krusk)-5
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Ft(,)127 5023 y(Ph)m(ys.)34 b(Rev.)f(Lett.,)g Fo(58)g
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58 57 bop -74 59 a Ft([55])49 b(J.)26 b(Shatah)g(&)g(W.A.)h(Strauss,)h
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(\(ftp://www.math.rutgers.edu/pub/so\013er\))-74 1575
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b(ound)35 b(state)g(and)f(instability)h(of)f(excite)-5
b(d)35 b(states)p Ft(,)d(in)g(preparation.)-74 3770 y([64])49
b(E.M.)29 b(Stein,)g(Singular)e(In)m(tegrals)i(and)f(Di\013eren)m
(tiabilit)m(y)d(Prop)s(erties)k(of)f(F)-8 b(unctions,)29
b(Princeton)g(Uni-)127 3919 y(v)m(ersit)m(y)34 b(Press)g(\(1970\))-74
4149 y([65])49 b(W.A.)26 b(Strauss,)i(Nonlinear)d(W)-8
b(a)m(v)m(e)27 b(Equations,)h(CBMS)f(Regional)c(Conference)28
b(Series)f(in)e(Mathemat-)127 4299 y(ics)32 b(#7)h(AMS)g(\(1985\))-74
4528 y([66])49 b(D.M.)30 b(Stuart,)g Fr(Minimal)i(p)-5
b(erio)g(ds)31 b(for)h(solutions)g(of)h(some)e(classic)-5
b(al)31 b(\014eld)h(e)-5 b(quations)p Ft(,)30 b(SIAM)h(Journal)127
4678 y(of)h(Mathematical)e(Analysis,)j(to)f(app)s(ear.)-74
4907 y([67])49 b(A.)36 b(V)-8 b(anderbau)m(whede)39 b(&)d(G.)g(Io)s
(oss)g Fr(Center)i(manifold)f(the)-5 b(ory)39 b(in)f(in\014nite)f
(dimensions)p Ft(,)f(Dynamics)127 5057 y(Rep)s(orted)c
Fo(2)h Ft(\(1990\))1901 5306 y(58)p eop
%%Page: 59 59
59 58 bop -74 59 a Ft([68])49 b(C.E.)39 b(W)-8 b(a)m(yne,)42
b Fr(Perio)-5 b(dic)40 b(and)g(quasi-p)-5 b(erio)g(dic)39
b(solutions)h(of)h(nonline)-5 b(ar)39 b(wave)h(e)-5 b(quations)40
b(via)g(KAM)127 208 y(the)-5 b(ory)p Ft(,)33 b(Comm)m(un.)f(Math.)h(Ph)
m(ys.)h Fo(127)f Ft(\(1990\))e(479)-74 441 y([69])49
b(A.)42 b(W)-8 b(einstein,)45 b Fr(Perio)-5 b(dic)43
b(nonline)-5 b(ar)43 b(waves)g(on)h(a)f(half-line)e Ft(Comm)m(un.)h
(Math.)h(Ph)m(ys.)h Fo(99)f Ft(\(1985\))127 590 y(383;)32
b(Erratum)g Fo(107)g Ft(\(1986\))g(177.)-74 822 y([70])49
b(M.I.)33 b(W)-8 b(einstein,)33 b Fr(Lyapunov)i(stability)g(of)g(gr)-5
b(ound)35 b(states)g(of)g(nonline)-5 b(ar)34 b(disp)-5
b(ersive)34 b(evolution)g(e)-5 b(qua-)127 972 y(tions)p
Ft(,)32 b(Comm)m(un.)g(Pure)h(Appl.)g(Math.)g Fo(39)f
Ft(\(1986\))g(51{68.)-74 1204 y([71])49 b(V.)31 b(W)-8
b(eissk)m(opf)33 b(&)e(E.)h(Wigner,)f Fr(Ber)-5 b(e)g(chnung)32
b(der)i(nat)q(\177)-51 b(urlichen)33 b(Linienbr)-5 b(eite)33
b(auf)h(Grund)g(der)g(Dir)-5 b(ac-)127 1354 y(schen)34
b(Lichtthe)-5 b(orie)p Ft(,)32 b(Z.)g(Ph)m(ys.)j Fo(63)d
Ft(\(1930\))g(54{73.)-74 1586 y([72])49 b(K.)d(Y)-8 b(a)5
b(jima,)48 b Fq(W)765 1550 y Fn(k)r(;p)862 1586 y Fr(-c)-5
b(ontinuity)48 b(of)g(wave)e(op)-5 b(er)g(ators)47 b(for)h(Schr\177)-50
b(odinger)46 b(op)-5 b(er)g(ators)p Ft(,)49 b(J.)e(Math.)g(So)s(c.)127
1736 y(Japan)32 b Fo(47)h Ft(\(1995\))e(551-581.)-74
1968 y([73])49 b(F.)32 b(Zhang,)g(Y.S.)h(Kivshar,)f(B.A.)h(Malomed)e(&)
i(L.)f(V\023)-49 b(azquez,)34 b Fr(Kink)g(c)-5 b(aptur)g(e)35
b(by)g(a)g(lo)-5 b(c)g(al)34 b(impurity)h(in)127 2118
y(the)g(sine)f(Gor)-5 b(don)34 b(mo)-5 b(del)p Ft(,)32
b(Ph)m(ys.)j(Lett.)d Fo(A159)h Ft(\(1991\))e(318{322.)1901
5306 y(59)p eop
%%Trailer
end
userdict /end-hook known{end-hook}if
%%EOF
