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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
a-adic solenoid      322
Absolutely continuous function      64
absorption operator      362
Abstract, Cauchy problem      see “Cauchy problem”
Abstract, control system      see “Control system”
Abstract, delay differential equation      see “Delay differential equation”
Abstract, Dyson — Phillips series      198
Abstract, extrapolation space      125
Abstract, Favard space      130
Abstract, H?older space      130
Abstract, second-order Cauchy problem      see “Second-order Cauchy problem”
Abstract, Volterra operator      162 182 195
Adjoint operator      517
Algebra homomorphism      58
Approximate, eigenvalue      242
Approximate, eigenvector      242
Approximate, point spectrum      242
Arveson Spectrum      285 287
Autonomous system      535
Balanced exponential growth      336 358
Banach lattice      353
Bernstein operators      224
Bochner integral      523
Bohr compactification      322
Boltzmann, operator      362
Boundary condition      256
Boundary condition, Dirichlet      397
Boundary condition, elastic barrier      397
Boundary condition, Neumann      397
Boundary condition, Ventcel      398
Boundary point      396
Boundary spectrum      116 282 324 356
Boundary spectrum, cyclic      357
Calkin algebra      248
Cauchy problem      17 84 145 150 295 347 368 419
Cauchy problem, controlled      452
Cauchy problem, inhomogeneous      436
Cauchy problem, mild solution of      146
Cauchy problem, nonautonomous      227 477
Cauchy problem, second-order      see “Second-order Cauchy problem”
Cauchy problem, solution of      145
Cauchy problem, well-posed      151
Cesaro means      337
Chaos paradigm      538
Chaos theory      536
Character group      313 320
Characteristic equation      256 335 352 388 427 451
Characteristic equation, generalized      431
Characteristic function      231 256 352
Chernoff product formula      220
Classical solution      145 368 420 436 477
Closed convex hull      511
Closure of an operator      516
Collisionless transport operator      362
Compact operator group      319
Compact resolvent      117
Compact semigroup      308
Complex inversion formula      233
Control system, approximately p-controllable      457
Control system, approximately q-observable      467
Control system, exactly p-controllable      456
Control system, exactly p-null controllable      457
Control system, exactly q-observable      467
Control system, exponentially detectable      471
Control system, exponentially stabilizable      468
Control system, external stability of      475
Control system, input–output stability of      475
Control system, internal stability of      475
Control system, similar      466
Control system, strongly stabilizable      472
Control system, transfer function of      474
Control, Banach space      452
Control, feedback      453
Control, function      452
Control, operator      452
Controllability      453
Controllability map      456
Controlled abstract wave system .........      455
Controlled heat equation      453 459 465 468 471 474 476
Controlled wave equation      454 460 465 468 473 474
Convex compactness property      525
Convolution of functions      164 527 530
Convolution of sequences      527
Core of an operator      52 58 517
Damping operator      367
Delay, differential equation      93 255 420
Delay, operator      420
Derivation      58
Determinism      531
Deterministic system      535
Diffusion semigroup      68 69 177 224 384
Domain of an operator      49 53 519
Dominant eigenvalue      13 331 360
Duality set      87
Dynamical system      6
Dyson — Phillips series      163 186
Eigenvalue      241
Eigenvalue, dominant      13 331 360
Eigenvalue, simple      13
Eigenvector      241
Elastic operator      367
Entire vector      81
Essential growth bound      258
Essential norm      249
Essential range      31 524
Essential spectral radius      249
Essential spectrum      248
Essential supremum      32 524
Evolution equation      531
Evolution family      478
Evolution family with exponential dichotomy      480
Evolution family, exponentially bounded      479
Evolution family, exponentially stable      479
Evolution family, hyperbolic      480
Evolution semigroup      481
Extended transfer function      474
Extension of an operator      516
External stability      475
Extrapolation space      125 126
Favard space      130
Favard space, extrapolated      190
Feedback control      453
Feedback operator      453 468
Flow      91
Formula, Chernoff product      220
Formula, complex inversion      233
Formula, Fourier inversion      406 527
Formula, Phragm?en inversion      236
Formula, Post — Widder      223 231 236
Formula, Trotter product      227
Formula, variation of parameters.      162 183 186 196 198 425 436
Fourier transform      406 526
Fourier transform, inversion theorem      406 527
Fourier transform, uniqueness theorem      527
Fractional power      137
Fredholm, domain      248
Fredholm, operator      248
Function, (strongly) measurable      523
Function, absolutely continuous      64
Function, additive      6
Function, almost periodic      317
Function, Bochner integrable      523
Function, control      452
Function, essentially bounded      524
Function, observation      452
Function, rapidly decreasing      405
Function, simple      522
Function, subadditive      251
Functional calculus      231 284 285
Functional equation      2 6 497
Gaussian semigroup      69
Generator      17 47 49 79
Graph      515
Graph, norm      52 515
Green’s function      391 485
Group, generator of      79
Group, induced by flow      91
Group, one-parameter      14 535
Group, periodic      35
Group, rotation      35
Group, solenoidal      320
Group, strongly continuous      37 78
Growth bound of a semigroup      40 250 299
Growth bound of an evolution family      479
Heat semigroup      69
Hilbert direct sum      511
Holder space, abstract      130
Holder space, classical      510
Ideal      309
Impulse response function      474
Inhomogeneous abstract Cauchy problem      436
Initial state      452
Initial value problem      145
Input      452
Input–output stability      475
Integral solution      156
Integral, Bochner      523
Integrated semigroup      153
Internal stability      475
Isolated singularities      246
Isometric limit semigroup      263
Landau — Kolmogorov inequality      59
Laplace transform      530
Laplace transform, convolution theorem      530
Laplace transform, uniqueness theorem      530
Left multiplicative perturbation      201
Left translation      33
Liapunov stability theorem      12
Linear dynamical system      6 14
Mean ergodic projection      338
Mild solution      146 436
Moment inequality      141
Motion      533
Multiplication, operator      25 31 218
Multiplication, semigroup      27 32 65 120 217
Non-quasi-analytic weight      289
Nonautonomous abstract Cauchy problem      227 477
Nonautonomous abstract Cauchy problem, hyperbolic case      479
Nonautonomous abstract Cauchy problem, parabolic case      479
Nonautonomous abstract Cauchy problem, solution of      477 478
Nonautonomous abstract Cauchy problem, well-posed      477
Nonautonomous Cauchy problem mild solution of      488
Nonobservable subspace      468
Observability      453
Observability, map      466
Observation, Banach space      452
Observation, function      452
Observation, operator      452
One-parameter group      9
One-parameter semigroup      8
Operator with compact resolvent      117
Operator, adjoint      61 517
Operator, approximate eigenvalue of      242
Operator, approximate eigenvector of      242
Operator, approximate point spectrum of      242
Operator, bounded      517
Operator, central      46
Operator, closable      82 516
Operator, closed      515
Operator, closure      516
Operator, control      452
Operator, core of      52
Operator, damping      367
Operator, degenerate      383 390
Operator, delay      420
Operator, delay differential      92 255 420
Operator, differential      91
Operator, dissipative      82
Operator, domain of      49
Operator, doubly power bounded      285
Operator, eigenvalue of      241
Operator, elastic      367
Operator, elliptic      409
Operator, feedback      453
Operator, fractional power of      137
Operator, Fredholm      248
Operator, Hille — Yosida      87
Operator, homogeneous      409
Operator, implemented      20
Operator, infinitely divisible      23
Operator, kernel of      516
Operator, local      33 46
Operator, multiplication      25 31
Operator, nondegenerate      383
Operator, normal      30 105 282
Operator, observation      452
Operator, part of      60 124 245 261
Operator, point spectrum of      241
Operator, range of      517
Operator, relatively bounded      169
Operator, relatively compact      179
Operator, residual spectrum of      243
Operator, resolvent of      15 55 239
Operator, resolvent set of      15 55 239
Operator, second-order differential      93 383
Operator, sectorial      96
Operator, self-adjoint      30 90 106 324 459 460 506
Operator, skew-adjoint      89
Operator, spectral bound of      57 250
Operator, spectral decomposition of      244
Operator, spectrum of      15 55 239
Operator, system      452
Operator, uniformly elliptic      411 489
Operator, Volterra      162 182 195
Operator, weakly closed      515
Optimal regularity      442
Optimal space regularity      447
Orbit      6
Orbit, map      36 48
Orbit, reversible      315
Orbit, stable      315
Output      452
Output injection operator      471
Period      266
Perturbation, additive      157 169 201
Perturbation, Desch — Schappacher      182
Perturbation, Miyadera — Voigt      195
Perturbation, multiplicative      201
Phragm?en inversion formula      236
Plancherel’s equation      407
Point spectrum      241
Pole      246
Pole, algebraic multiplicity of      246
Pole, algebraically simple      246
Pole, first-order      246
Pole, geometric multiplicity of      246
Population equation      348 419 434
Post — Widder inversion formula      223 231 236
Principal part      409
Principle of uniform boundedness      512
Pseudoresolvent      206
quantum mechanics      536
reachability space      466
reactor problem      361
Relativity      536
Residual spectrum      243
Residue      246
Resolvent      15 239
Resolvent map      239
Resolvent map, isolated singularities of      246
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