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Engel K.-J., Nagel R. — One-Parameter Semigroups for Linear Evolution Equations
Engel K.-J., Nagel R. — One-Parameter Semigroups for Linear Evolution Equations



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Название: One-Parameter Semigroups for Linear Evolution Equations

Авторы: Engel K.-J., Nagel R.

Аннотация:

This book gives an up-to-date account of the theory of strongly continuous one-parameter semigroups of linear operators. It includes a systematic discussion of the spectral theory and the long-term behavior of such semigroups. A special feature of the text is an unusually wide range of applications, to ordinary and partial differential operators, delay and Volterra equations and to control theory, et cetera, and an emphasis on philosophical motivation and the historical background.. "The book is written for students, but should also be of value for researchers interested in this field.


Язык: en

Рубрика: Математика/Анализ/Функциональный анализ/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1999

Количество страниц: 586

Добавлена в каталог: 09.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Resolvent map, poles of      246
Resolvent map, residue of      246
Resolvent, compact      117
Resolvent, equation      239
Resolvent, integral representation      55
Resolvent, operator      47
Resolvent, pseudo      206
Resolvent, set      15 47 239
Riemann — Lebesgue lemma      406 526
Right multiplicative perturbation      201
Right translation      33
Rotation group      35 320
Scattering operator      362
Schwartz space      405
Second-order Cauchy problem      367
Second-order Cauchy problem, controlled      455
Second-order Cauchy problem, extended      374
Second-order Cauchy problem, overdamped      370
Second-order Cauchy problem, solution of      368
Semiflow      95
Semiflow, uniquely ergodic      345
Semigroup      308
Semigroup with balanced exponential growth      336 346 358 364
Semigroup, $C_0$      36
Semigroup, abstract Sobolev space of      124 126
Semigroup, adjoint      43
Semigroup, analytic      101
Semigroup, asymptotically norm-continuous      282
Semigroup, bounded      40
Semigroup, compact      308
Semigroup, contractive      40
Semigroup, differentiable      109
Semigroup, diffusion      68 69 177 224 384
Semigroup, dual      62
Semigroup, essential growth bound of      258
Semigroup, essentially compact      336
Semigroup, eventually compact      117
Semigroup, eventually differentiable      109
Semigroup, eventually norm-continuous      112
Semigroup, exponentially stable      298
Semigroup, extrapolation space of      126
Semigroup, fixed space      337
Semigroup, generator of      47
Semigroup, growth bound of      40 250
Semigroup, hyperbolic      13 24 305
Semigroup, immediately compact      117
Semigroup, immediately differentiable      109
Semigroup, immediately norm-continuous      112
Semigroup, irreducible      357
Semigroup, isometric      40
Semigroup, isometric limit      263
Semigroup, law      14 536
Semigroup, matrix      8
Semigroup, mean ergodic      338
Semigroup, multiplication      27 122 217
Semigroup, nilpotent      35 120 123
Semigroup, norm-continuous      16
Semigroup, one-parameter      14 535
Semigroup, orbit of      6
Semigroup, periodic      266
Semigroup, positive      322 353
Semigroup, product      44 64
Semigroup, quasi-compact      332
Semigroup, quasicontractive      76
Semigroup, quotient      43 61
Semigroup, rescaled      43 60
Semigroup, semitopological      308
Semigroup, similar      10 59
Semigroup, stable      12
Semigroup, strongly continuous      36
Semigroup, strongly stable      296 323 326
Semigroup, subspace      43 60
Semigroup, sun dual      62 134
Semigroup, totally ergodic      345
Semigroup, translation      34 35
Semigroup, type of      40
Semigroup, uniformly continuous      16
Semigroup, uniformly exponentially stable      18 296
Semigroup, uniformly mean ergodic      342
Semigroup, uniformly stable      296
Semigroup, weak* generator of      61
Semigroup, weak*-continuous      43
Semigroup, weak*-stable      298
Semigroup, weakly continuous      40
Semigroup, weakly stable      296
Semigroups, isomorphic      43
Semigroups, similar      43
Semitopological semigroup      308
Similar control systems      466
Sobolev space of vector-valued functions      525
Sobolev space, abstract      124 126 129
Sobolev space, classical      407
Sobolev, embedding theorem      408
Sobolev, tower      126
Solution, classical      145 420 436
Solution, integral      156
Solution, mild      146 436
Space of strong continuity      132
Spectral bound      57 250
Spectral bound, equal growth bound condition      281
Spectral bound, function      430
Spectral decomposition      244
Spectral inclusion theorem      276
Spectral mapping theorem      19 243 270 271
Spectral mapping theorem for eventually norm-continuous semigroups      280
Spectral mapping theorem for evolution semigroups      483
Spectral mapping theorem for the point and residual spectrum      277
Spectral mapping theorem for the resolvent      243
Spectral mapping theorem, weak      32 271 283
Spectral projection      244
Spectral radius      241
Spectral theorem      30
Spectrum      15
Spectrum, approximate point      242
Spectrum, essential      248
Spectrum, point      241
Spectrum, residual      243
Stability, condition      212 227
Stability, exponential      298
Stability, external      475
Stability, input–output      475
Stability, internal      475
Stability, Liapunov      12
Stability, strong      296 323 326
Stability, uniform      296
Stability, uniform exponential      18 296
Stability, weak      296
Stability, weak*      298
Stabilizability      453
State space      368 452 533
Streaming semigroup      363
Strong operator topology      512
Structural damping      372
Subspace of strong continuity      62
Sun dual      62
Support of a function      25
system      533
System operator      452
System, autonomous      535
System, deterministic      535
Tensor product      520
Theorem, Arendt — Batty — Lyubich — Vu      326
Theorem, Banach — Alaoglu      511
Theorem, Datko — Pazy      300
Theorem, Desch — Schappacher      182
Theorem, Gearhart — Greiner — Pruss      302
Theorem, Gelfand      521
Theorem, Greiner      366
Theorem, Halmos — von Neumann      322
Theorem, Hille — Yosida      73
Theorem, Jacobs — Glicksberg — DeLeeuw      314
Theorem, Kre?n      511
Theorem, Liapunov      12 19 302 346
Theorem, Lumer — Phillips      83
Theorem, Miyadera — Voigt      195
Theorem, Perron — Frobenius      356
Theorem, Plancherel      407 529
Theorem, Sobolev’s embedding      408
Theorem, Stone      89
Theorem, Trotter — Kato      209 212
Time      533
Topology, strong operator      512
Topology, uniform operator      512
Topology, weak      511
Topology, weak operator      512
Topology, weak*      511
Transfer function      474
Translation, group      34
Translation, property      95 422
Translation, semigroup      33—35
Transport, equation      361
Transport, operator      362
Transport, semigroup      363
Trotter product formula      227
Uniform operator topology      512
Variation of parameters formula      162 183 186 196 198 425 436
Vector lattice      353
Volterra, integro-differential equation      449
Volterra, operator      162 182 195
Weak derivative      407 413
Weak operator topology      512
Weak spectral mapping theorem      32 271 283
Weak topology      511
Weak*, generator      61
Weak*, topology      511
wronskian      391
Yosida approximation      74 205 214
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