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Engel K.-J., Nagel R. — One-Parameter Semigroups for Linear Evolution Equations (preliminary version of 10 September 1998)
Engel K.-J., Nagel R. — One-Parameter Semigroups for Linear Evolution Equations (preliminary version of 10 September 1998)

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Название: One-Parameter Semigroups for Linear Evolution Equations (preliminary version of 10 September 1998)

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/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1998

Количество страниц: 517

Добавлена в каталог: 07.12.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
a-adic solenoid      329
Abstract Cauchy problem      see “Cauchy problem”
Abstract control system      440
Abstract Dyson-Phillips series      211
Abstract second-order Cauchy problem      364
Adjoint operator      490
Algebra homomorphisms      79
Approximate eigenvalue      254
Approximate eigenvector’      254
Approximate point spectrum      254
Arveson Spectrum      293 295
Bohr compactification      329
Boundary spectrum      331
Calkin algebra      260
Cauchy problem      104 161 166 305 352 364 413
Cauchy problem, hyperbolic case      466
Cauchy problem, mild solution of      162
Cauchy problem, parabolic case      466
Cauchy problem, solution of      161
Cauchy problem, well-posed      167 465
Cesaro means      342 343
Character group      321 327
Characteristic equation      267 341 420 424
Characteristic function      267
Chernoff product formula      232
Classical solution      428
Closed convex hull      343
Closure of an operator      489
Compact operator groups      327
Compact semigroup      317
Complex inversion formula      246
Control Banach space      440
Control function      440
Control operator      440
Control system      440
Control system, approximately g-observable      454
Control system, approximately p-controllable      445
Control system, exactly g-observable      454
Control system, exactly p-controllable      444
Control system, exactly p-null controllable      445
Control system, exponentially detectable      458
Control system, exponentially stabilizable      456
Control system, external stability of      461
Control system, input-output stability of      461
Control system, internal stability of      461
Control system, strongly stabilizable      458
Control system, transfer function of      460
Controllability map      444
Controlled abstract wave system      442
Controlled heat equation      441 446 452 455 458 461 464
Controlled wave equation      442 447 452 455 459 461
Convolution of functions      177 495
Convolution of sequences      495
Core of an operator      74 79 490
Damping operator      364
Delay differential equation      112 266 414
Derivation      79
Diffusion semigroup      90
Diffusion, semigroup      88
Discrete spectrum      351
Distributional $\alpha$-derivative      399
Domain      70
Dominant eigenvalue      338
Duality set      107
Dyson — Phillips expansion      176
Dyson — Phillips series      199
Eigenvalue      254
Eigenvalue, dominant      36 338
Eigenvector      254
Elastic operator      364
Essential growth bound      269
Essential norm      260
Essential range      53
Essential spectral r adius      260
Essential spectrum      260
Essential supremum      54
Evolution family      465
Evolution family, exponentially bounded      467
Evolution family, exponentially stable      467
Evolution family, hyperbolic      467
Evolution family, with exponential dichotomy      467
Evolution semigroup      468
Extended transfer function      460
Extension of an operator      489
External stability      461
Extrapolation space      143
Favard space      147 203
Feedback operator      456
Flow      110
Fourier transform      495
Fredholm domain      260
Fredholm operator      260
Function, rapidly decreasing      396
Functional equation      26
Gaussian semigroup      90
Generator      40 69 70 99
Graph      489
Graph norm      74 489
Group, generator of      99
Group,induced by flow      110
Group,one-parameter      37
Group,periodic      57
Group,rotation      57
Group,solenoidal      327
Group,strongly continuous      59 99
Growth bound      62 262 308
Growth bound of an evolution family      466
Heat semigroup      90
Holder space      147
Ideal      317
Impulse response function      460
Inhomogeneous abstiact Cauchy problem      428
inhomogeneous differential equations      427
Initial state      440
Initial value problem      161
Input-output stability      461
Integrated semigroup      168
Internal stability      461
Isolated singularities      258
Isometric limit semigroup      274
Landau — Kolmogoroff Inequality      79
Laplace transform      494
Left multiplicative perturbation      213
Left translation      55
Left translation semigroup      56
Liapunov stability theorem      35
Linear dynamical system      29
Markov operator      338
Mean eigodic projection      344
Mild solution      162 428
Moment inequality      160
Multiplication operator      47
Multiplicative perturbations      213
Non-observable subspace      455
Nonautonomous Cauchy problem      see “Cauchy problem”
Observability map      453
Observation      440
Observation Banach space      440
Observation operator      440
One-parameter group      32
One-parameter semigroup      32
Operator, adjoint      490
Operator, approximate eigenvalue of      254
Operator, approximate eigenvector of      254
Operator, approximate point spectrum of      254
Operator, bounded      490
Operator, closable      489
Operator, closed      489
Operator, closure      489
Operator, core of      74
Operator, delay differential      111 266 414
Operator, differential      110
Operator, dissipative      102
Operator, domain of      70
Operator, doubly power bounded      294
Operator, eigenvalue of      254
Operator, fractional power of      154
Operator, Fredholm      260
Operator, Hille — Yosida      106
Operator, implemented      43
Operator, infinitely divisible      46
Operator, local      55 68
Operator, Markov      338
Operator, multiplication      47 53
Operator, part of      81 142 257 272
Operator, point spectrum of      254
Operator, relatively bounded      183
Operator, relatively compact      192
Operator, residual spectrum of      255
Operator, resolvent of      38 76 251
Operator, resolvent set of      38
Operator, second-order differential      113
Operator, sectorial      115
Operator, skew adjoint      108
Operator, spectral bound of      78 262
Operator, spectral decomposition of      256
Operator, spectrum of      38 76 251
Operator, Volteira      175 195 208
Operator, weakly closed      489
Operator, with compact resolvent      135
Orbit maps      58 69
Orbit, reversible      323
Orbit, stable      323
Order continuous norm      353
Output injection operator      458
Period      276
Perturbation, Desch — Schappacher      195
Perturbation, Miyadera — Voigt      208
Perturbation, multiplicative      213
Plancherel equation      399
Pliragmen inversion formula      249
Point spectrum      254
Pole      258
Pole, algebraic multiplicity of      258
Pole, algebraically simple      258
Pole, geometric multiplicity of      258
Pseudo resolvent      219
reachability space      453
Residual spectrum      255
Residue      258
Resolvent      38 251
Resolvent equation      252
Resolvent map      251
Resolvent map, isolated singularities of      258
Resolvent map, poles of      258
Resolvent map, residue of      258
Resolvent operator      69
Resolvent set      38 69 251
Resolvent, integral representation      76
Right multiplicative perturbation      213
Right tr anslation      55
Rotation group      57 327
Schwartz space      396
Second-order abstract Cauchy problem      see “Second-order Cauchy problem”
Semiflow      114
Semigroup      317
Semigroup dual      82
Semigroup law      37
Semigroup, abstract Sobolev space of      142 143
Semigroup, adjoint      65
Semigroup, analytic      119
Semigroup, bounded      62
Semigroup, Co      58
Semigroup, compact      135 317
Semigroup, contractive      62
Semigroup, differentiable      128
Semigroup, diffusion      88 90
Semigroup, essential growth bound of      269
Semigroup, essentially compact      342
Semigroup, eventually compact      135
Semigroup, eventually differ entiable      128
Semigroup, eventually norm continuous      131
Semigroup, exponentially stable      308
Semigroup, extrapolation space of      143
Semigroup, fixed space      343
Semigroup, generator of      69
Semigroup, growth bound of      62
Semigroup, hyperbolic      36 46 314
Semigroup, immediately compact      135
Semigroup, immediately differ entiable      128
Semigroup, immediately norm continuous      131
Semigroup, isometric limit      274
Semigroup, matrix      32
Semigroup, mean ergodic      344
Semigroup, multiplication      49 140
Semigroup, nilpotent      57 138 141
Semigroup, norm continuous      39
Semigroup, norm continuous at infinity      298
Semigroup, on a Hilbert space      42
Semigroup, on an operator algebra      43
Semigroup, one-parameter      37
Semigroup, orbit of      29
Semigroup, periodic      276
Semigroup, positive      329
Semigroup, product      66 85
Semigroup, quasi-compact      339
Semigroup, quasicontractive      96
Semigroup, quotient      65 81
Semigroup, reseated      65 80
Semigroup, semitopological      317
Semigroup, similar      80
Semigroup, stable      35
Semigroup, strongly continuous      58
Semigroup, strongly stable      306 330
Semigroup, subspace      65 80
Semigroup, sun dual      82 151
Semigroup, superstable      336
Semigroup, translation      57
Semigroup, type of      62
Semigroup, ultrapower      67 336
Semigroup, uniformly continuous      39
Semigroup, uniformly exponentially stable      41 306
Semigroup, uniformly mean ergodic      347
Semigroup, uniformly stable      306
Semigroup, weak *-continuous      65
Semigroup, weak *-generatoi of      82
Semigroup, weakly continuous      62
Semigroup, weakly stable      306
Semigroup, with balanced exponential growth      342
Semigroups, isomorphic      65
Semigroups, similar      65
Semitopological semigroup      317
Similar control system      453
Sobolev lemma      402
Sobolev space      142 143 146 399
Sobolev tower      144
Solution, classical      428
Solution, mild      428
Spectral bound      78 262
Spectral decomposition      256
Spectral equal growth bound condition      290
Spectral inclusion theorem      286
Spectral mapping theorem      41 255 281
Spectral mapping theorem for eventually norm continuous semigroups      290
Spectral mapping theorem for the point and residual spectrum      287
Spectral mapping theorem for the resolvent      255
Spectral mapping theorem, weak      55 281
Spectral projection      256
Spectral radius      253
Spectral theorem      53
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