One-Parameter Semigroups for Linear Evolution Equations

Front Cover
Springer Science & Business Media, 2000 - Mathematics - 586 pages
1 Review
The theory of one-parameter semigroups of linear operators on Banach spaces started in the ?rst half of this century, acquired its core in 1948 with the Hille–Yosida generation theorem, and attained its ?rst apex with the 1957 edition of Semigroups and Functional Analysis by E. Hille and R.S. Phillips. In the 1970s and 80s, thanks to the e?orts of many di?erent schools,thetheoryreachedacertainstateofperfection,whichiswellrep- sented in the monographs by E.B. Davies [Dav80], J.A. Goldstein [Gol85], A. Pazy [Paz83], and others. Today, the situation is characterized by manifold applications of this theory not only to the traditional areas such as partial di?erential eq- tions or stochastic processes. Semigroups have become important tools for integro-di?erentialequationsandfunctionaldi?erentialequations,inqu- tum mechanics or in in?nite-dimensional control theory. Semigroup me- ods are also applied with great success to concrete equations arising, e.g., in population dynamics or transport theory. It is quite natural, however, that semigroup theory is in competition with alternative approaches in all of these ?elds, and that as a whole, the relevant functional-analytic toolbox now presents a highly diversi?ed picture. At this point we decided to write a new book, re?ecting this situation but based on our personal mathematical taste. Thus, it is a book on se- groups or, more precisely, on one-parameter semigroups of bounded linear operators. In our view, this re?ects the basic philosophy, ?rst and strongly emphasized by A. Hadamard (see p. 152), that an autonomous determin- tic system is described by a one-parameter semigroup of transformations.
  

What people are saying - Write a review

We haven't found any reviews in the usual places.

Contents

III
1
IV
2
V
6
VI
14
VII
24
IX
30
X
33
XI
36
LXXIV
345
LXXV
347
LXXVI
348
LXXVII
349
LXXVIII
353
LXXIX
358
LXXX
361
LXXXIII
364

XII
37
XIII
42
XIV
46
XV
47
XVI
48
XVII
59
XIX
65
XX
70
XXI
71
XXII
82
XXIII
89
XXIV
96
XXVI
109
XXVII
112
XXVIII
117
XXIX
120
XXX
123
XXXI
124
XXXII
129
XXXIII
137
XXXIV
145
XXXV
154
XXXVI
157
XXXVII
169
XXXVIII
182
XL
192
XLI
195
XLII
201
XLIII
205
XLIV
206
XLV
209
XLVI
214
XLVII
219
XLIX
231
L
236
LI
238
LII
239
LIII
250
LV
259
LVI
266
LVII
270
LIX
275
LX
283
LXI
289
LXII
293
LXIII
295
LXIV
296
LXVI
299
LXVII
305
LXVIII
308
LXX
312
LXXI
315
LXXII
329
LXXIII
337
LXXXIV
367
LXXXV
369
LXXXVI
372
LXXXVII
374
LXXXVIII
382
LXXXIX
383
XC
384
XCI
388
XCII
390
XCIII
400
XCIV
403
XCV
404
XCVI
405
XCVII
408
XCVIII
411
XCIX
419
CI
420
CII
424
CIII
428
CIV
435
CVI
436
CVII
442
CVIII
447
CIX
452
CXI
456
CXII
466
CXIII
468
CXIV
473
CXV
476
CXVI
477
CXVIII
481
CXIX
487
CXX
492
CXXI
496
CXXII
497
CXXIII
500
CXXIV
502
CXXV
506
CXXVI
509
CXXVII
515
CXXVIII
522
CXXIX
526
CXXX
530
CXXXI
531
CXXXII
533
CXXXIII
536
CXXXIV
538
CXXXV
546
CXXXVI
549
CXXXVII
553
CXXXVIII
555
CXXXIX
577
CXL
580
Copyright

Common terms and phrases

Popular passages

Page 553 - the creation of this world is the combined work of necessity and mind. Mind, the ruling power, persuaded necessity to bring the greater part of created things to perfection (...). But if a person will truly tell of the way in which the work was accomplished. he must include the variable cause as well

References to this book

Funktionalanalysis
Dirk Werner
No preview available - 2007
All Book Search results »

Bibliographic information