Perturbation Theory for Linear Operators

Front Cover
Springer Science & Business Media, Feb 15, 1995 - Mathematics - 623 pages
1 Review
In view of recent development in perturbation theory, supplementary notes and a supplementary bibliography are added at the end of the new edition. Little change has been made in the text except that the para graphs V- 4.5, VI- 4.3, and VIII- 1.4 have been completely rewritten, and a number of minor errors, mostly typographical, have been corrected. The author would like to thank many readers who brought the errors to his attention. Due to these changes, some theorems, lemmas, and formulas of the first edition are missing from the new edition while new ones are added. The new ones have numbers different from those attached to the old ones which they may have replaced. Despite considerable expansion, the bibliography i" not intended to be complete. Berkeley, April 1976 TosIO RATO Preface to the First Edition This book is intended to give a systematic presentation of perturba tion theory for linear operators. It is hoped that the book will be useful to students as well as to mature scientists, both in mathematics and in the physical sciences.
 

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Perturbation theory for linear operators

Contents

II
1
III
2
IV
3
V
4
VI
6
VII
7
VIII
8
IX
10
CLXI
270
CLXII
272
CLXIII
274
CLXIV
275
CLXV
276
CLXVI
277
CLXVII
278
CLXVIII
281

X
11
XI
12
XII
13
XIII
14
XIV
15
XV
16
XVI
18
XVII
19
XVIII
20
XIX
22
XX
23
XXI
25
XXII
27
XXIII
28
XXIV
29
XXV
31
XXVI
32
XXVII
34
XXVIII
36
XXIX
38
XXX
40
XXXI
43
XXXII
44
XXXIII
46
XXXIV
47
XXXV
48
XXXVI
49
XXXVII
51
XXXVIII
52
XXXIX
54
XL
55
XLI
56
XLII
58
XLIII
60
XLIV
62
XLV
63
XLVI
65
XLVII
66
XLVIII
67
XLIX
69
L
70
LI
72
LII
73
LIII
74
LIV
77
LV
81
LVI
83
LVII
85
LVIII
86
LIX
88
LX
89
LXI
91
LXII
93
LXIII
94
LXIV
97
LXV
98
LXVI
99
LXVII
102
LXVIII
104
LXX
106
LXXII
108
LXXIII
110
LXXIV
111
LXXV
113
LXXVI
115
LXXVII
116
LXXVIII
117
LXXIX
120
LXXX
121
LXXXI
122
LXXXII
124
LXXXIV
126
LXXXV
127
LXXXVI
129
LXXXVII
132
LXXXVIII
134
LXXXIX
136
XC
137
XCI
140
XCIII
142
XCIV
145
XCV
146
XCVI
149
XCVII
153
XCVIII
154
XCIX
155
C
157
CI
158
CII
160
CIII
163
CIV
164
CV
165
CVI
166
CVII
167
CVIII
171
CIX
172
CX
176
CXII
178
CXIII
180
CXIV
183
CXV
185
CXVI
187
CXVII
189
CXVIII
191
CXIX
194
CXX
196
CXXI
197
CXXII
199
CXXIII
200
CXXIV
201
CXXV
205
CXXVI
206
CXXVII
208
CXXVIII
209
CXXIX
210
CXXX
212
CXXXI
213
CXXXII
214
CXXXIII
215
CXXXIV
216
CXXXV
218
CXXXVI
221
CXXXVII
223
CXXXVIII
225
CXXXIX
227
CXL
229
CXLI
232
CXLII
236
CXLIII
239
CXLIV
241
CXLV
242
CXLVI
244
CXLVII
246
CXLVIII
248
CXLIX
249
CL
251
CLII
254
CLIII
256
CLIV
257
CLV
260
CLVI
262
CLVII
264
CLVIII
267
CLX
269
CLXIX
287
CLXX
289
CLXXI
290
CLXXII
291
CLXXIII
293
CLXXIV
297
CLXXV
299
CLXXVI
302
CLXXVII
305
CLXXVIII
308
CLXXIX
310
CLXXX
313
CLXXXI
315
CLXXXII
318
CLXXXIII
319
CLXXXIV
321
CLXXXV
322
CLXXXVI
323
CLXXXVII
325
CLXXXVIII
326
CLXXXIX
328
CXC
331
CXCI
334
CXCII
336
CXCIII
338
CXCIV
340
CXCV
341
CXCVI
343
CXCVII
346
CXCVIII
348
CXCIX
352
CC
353
CCI
356
CCII
360
CCIII
361
CCIV
364
CCV
365
CCVI
366
CCVII
368
CCVIII
371
CCIX
372
CCX
373
CCXI
375
CCXII
377
CCXIII
379
CCXIV
381
CCXV
383
CCXVI
385
CCXVII
387
CCXVIII
389
CCXIX
390
CCXX
392
CCXXI
393
CCXXII
395
CCXXIII
398
CCXXIV
401
CCXXV
403
CCXXVI
404
CCXXVII
407
CCXXVIII
408
CCXXIX
410
CCXXX
413
CCXXXI
414
CCXXXII
416
CCXXXIV
419
CCXXXV
421
CCXXXVI
422
CCXXXVII
423
CCXXXVIII
426
CCXXXIX
427
CCXL
431
CCXLI
433
CCXLII
437
CCXLIII
441
CCXLIV
444
CCXLV
445
CCXLVI
448
CCXLVII
453
CCXLVIII
455
CCXLIX
459
CCL
461
CCLI
462
CCLII
463
CCLIII
465
CCLIV
466
CCLV
470
CCLVI
473
CCLVII
474
CCLVIII
475
CCLIX
476
CCLX
479
CCLXI
480
CCLXII
482
CCLXIII
486
CCLXIV
488
CCLXV
489
CCLXVI
493
CCLXVII
495
CCLXVIII
497
CCLXIX
499
CCLXX
501
CCLXXI
502
CCLXXII
503
CCLXXIII
506
CCLXXIV
509
CCLXXV
511
CCLXXVI
513
CCLXXVII
514
CCLXXVIII
516
CCLXXIX
518
CCLXXX
521
CCLXXXI
523
CCLXXXII
525
CCLXXXIII
527
CCLXXXIV
529
CCLXXXV
531
CCLXXXVI
536
CCLXXXVII
537
CCLXXXVIII
540
CCLXXXIX
542
CCXC
545
CCXCI
549
CCXCII
553
CCXCIII
555
CCXCIV
557
CCXCV
558
CCXCVI
560
CCXCVII
563
CCXCVIII
565
CCXCIX
568
CCCI
569
CCCII
570
CCCIV
573
CCCV
574
CCCVII
575
CCCVIII
576
CCCIX
583
CCCX
593
CCCXI
596
CCCXII
606
CCCXIII
608
CCCXIV
612
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Page ii - Perturbation theory for linear operators is a collection of diversified results in the spectral theory of linear operators, unified more or less loosely by their common concern with the behavior of spectral properties when the operators undergo a small change.
Page xiv - Mathematically speaking, the method is equivalent to an approximate solution of the eigenvalue problem for a linear operator slightly different from a

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About the author (1995)

Biography of Tosio Kato

Tosio Kato was born in 1917 in a village to the north of Tokyo. He studied theoretical physics at the Imperial University of Tokyo. After several years of inactivity during World War II due to poor health, he joined the Faculty of Science at the University of Tokyo in 1951. From 1962 he was Professor of Mathematics at the University of California, Berkeley, where he is now Professor Emeritus.

Kato was a pioneer in modern mathematical physics. He worked in te areas of operator theory, quantum mechanics, hydrodynamics, and partial differential equations, both linear and nonlinear.

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