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Nagel R. — One-parameter semigroups of positive operators
Nagel R. — One-parameter semigroups of positive operators

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Название: One-parameter semigroups of positive operators

Автор: Nagel R.

Аннотация:

The book is organized as follows. We concentrate our attention on three subjects of semigroup theory: characterization, spectral theory and asymptotic behavior. By characterization , we understand the problem of describing special properties of a semigroup, such as positivity, through the generator. By spectral theory we mean the investigation of the spectrum of a generator. Asymptotic behavior refers to the orbits of the initial values under a given semigroup and phenomena such as stability.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1986

Количество страниц: 460

Добавлена в каталог: 08.12.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Abelian group      390
Abscissa of absolute convergence      103
Abscissa of holomorphy      101
Abscissa of simple convergence      103
Absolute value      235 239
Abstract Cauchy problem      4 26 98 336
Additive perturbation      43
Adjoint      16 400
Adjoint generator      17
Adjoint operator      16 64 77 141
Adjoint semigroup      16 77 400
Admissible function      154
AL-space      239
Algebra homomorphism      143
Algebraic ideal      118
Algebraic multiplicity      73 209 310
Algebraically simple pole      73 181 185 209 216 315
AM-space      239
Analytic semigroup      33
Approximate eigenvalue      64 314
Approximate eigenvector      64 314
Approximate point spectrum      64 394
Approximation theorems      32 44 81 116
Asymptotics      98 204 342 352 406
Automorphism group      146
Autonomous Cauchy problem      4 26
Banach lattice      235
Band      236
Band projection      237
Boundary spectrum      169 296 302 305 379 387
Bounded generator      2 7 54 129 247 255 288 376
Bounded holomorphic (of angle $\alpha$) semigroup      33 110
Bounded perturbation      44 307
Bounded semigroup      3
C*-algebra      117 369
Calkin algebra      73
Canonical half-norm      51 127
Cauchy problem      4 26
Center      246 272 279 288
Cesaro mean      346 406 408
Cesaro summable      93
Chain rule      136
Chapman — Kolmogorov equation      213
Characteristic equation      180 229 362
Characterization of generators      122 247 260 376
Classical Kato’s      139 258
Classical Sobolev space      19
Closable      5 52 128
Closable operator      5
Closed ideal      118 236
Closed operator      5
Closure      5 52 128
Cocycle      148
Commuting semigroup      24
Compact perturbation      215 319
Compact resolvent      40 73 130 166 177 305 318 336
Compact semigroup      40
Complex Banach lattice      243 260 288
Continuous flow      148 192 330
Continuous semiflow      144 192
Contraction semigroup      3 47 247 297 397
Contractive operator      47
Convolution semigroup      12
Core      5 46
Counter example      3 61 105 131 265 311
Cyclic      169 172 192 302 305 379 388
Cyclic spectrum      169 296 302 305 379 387
Datko’s theorem      108
Decomposition      68 325 351
Delay differential equation      219
Delay equation      356
Densely defined operator      4
Derivation      143
Differentiable semigroup      37 41
Differential equation      4
Differential operator      9 11 34 146 179 185 220 259 265 267 276 308 357
Diffusion semigroup      11
Disjointness preserving operator      281
Disjointness preserving semigroup      281
Dispersive      249
Dispersive operator      249
Dissipative      47
Dissipative operator      47
Distributional Kato’s      259
Doeblin’s condition      218 345
Domain      3 9 46
Domain of uniqueness      46
Dominant spectral value      177 210 217
Domination      269 371
Dual      16
Dunford — Pettis property      56
Eigenspace      64 86
Eigenvalue      64 387
Eigenvector      64 387
Elliptic differential operator      185 190 260 305 312
Elliptic operator      185 190 260 305 312
Ergodic projection      410 424
Essential growth bound      74 343
Essential spectral bound      73 214 318
Essential spectral radius      73 177 214 318
Essential spectrum      73
Eventually compact semigroup      40 209 211 214
Eventually differentiable semigroup      37 41
Eventually norm continuous semigroup      38 41 87 106 178 304 318 337 345
Exponential estimate      2
Exponential stability      99 227
F-product      20 298 314
F-product semigroup      20 74 192
F-product with respect to a semigroup      20 74 192
Face      388
Faithful subset      380
Fejer’s theorem      93
First order derivative      9 146 184 220 265 276 308 357
First order pole      73 180
Fixed space      343 374 380 414
Flow      143
Forcing term      112 340
Fourier transformation      12 91 252
Fourier transformation coefficient      80
Fredholm domain      73
Fredholm operator      73
Gateaux-derivative      50 136 257 283
Generalized characteristic equation      226 362
Generalized solution      99 112
Generalized solution of a Cauchy problem      99 112
Generator      3
Geometric multiplicity      73 310
Graph      5
Graph norm      5
Grothendieck space      55
Group      1 6 9 34 66 146 326 352 390
Group lattice homomorphism      202
Growth bound      2 6 60
Growth bound of a semigroup      2 6 60 74 99 130 168 204 295 334 343 400
Growth bound of mild solutions of a Cauchy problem      99
Growth bound of solutions of a Cauchy problem      99 204 336
Half-norm      51 127
Heat equation      13
Higher order derivative      267
Hilbert space      13 62 94 105 403
Hille — Yosida theorem      32
Holomorphic (of angle $\alpha$) semigroup      33 41 100 183 305 311
Homogeneous Cauchy problem      4 98
Homogeneous differential equation      4 98
Homomorphism lattice      120 243 244 281
Ideal      236
Identity preaerving semigroup      370 379 389 408 424
Identity preserving Schwarz map      370 379 381 408
Imaginary additively cyclic      172 192 302
Imaginary additively cyclic subset      172 192 297
Implemented semigroup      403
Induced semigroup      14 74 298 374
Inhomogeneous Cauchy problem      112 340
Inhomogeneous differential equation      112 340
Injective semiflow      193
Integral equation      363
Interpolation      335 348 352
Invariant face      388 410
Invariant ideal      182 303 306 317
Invariant ideals      182 303 306 317
Invariant subset      24 346
Inverse Fourier transformation      13 91
Irreducible      138 256 414
Irreducible semigroup      130 182 210 306 311 315 409
Isolated singularity      72
Jordan decomposition      384 389 420
Kakutani — Krein theorem      240 297 313 334
Kato’s equality      138 285 325
Kato’s inequality      139 285 325
Kernel operator      184 189 308 320 349 363 367
Krein — Rutman theorem      130 167 334
Laplace operator      13 34 100 110 139 168 185 205 250 258 338
Laplace transform      101 107
Laplacian      13 34 100 110 139 168 185 205 250 258 338
Lattice homomorphism semigroup      135 143 192 285 320
Lattice ideal      236
Lattice operator      120 242
Local operator      146 268 282 287
Locality      146 268 282 287
Locally compact Abelian group      390
Long term behavior      98 204 342 352 406
Lumer — Phillips theorem      53
Markov algebra homomorphism      143
Markov lattice homomorphism      120 192 200
Markov operator      120 191
Markov process      213
Markov semigroup      144 191
Markov transition function      213 347
Markovian semigroup      144 191
Matrix semigroup      7
Maximum principle      185 190
Mean-ergodic semigroup      346
Mild solution      99 112
Mild solution of a Cauchy problem      99 112
Modulus      136 257 278 281
Modulus semigroup      278 282
Multiplication operator      7 89 246 287
Multiplication semigroup      7 42 65 287
Multiplicative perturbation      131 141
Multiplicity      73
Multiplicity as a pole      73
n-positivity      370 403
Negative part      235
Nilpotent semigroup      11 41 74
Nilpotent translation semigroup      11 41 83 164
Norm continuous semigroup      38 41
Norm lattice      235
Normal conditional expectation      411 416
Normal linear functional      369
Normalized eigenvalue      389
One-parameter group      1 6 31
One-parameter semigroup      1
Operator semigroup      1 406
Order bounded      238
Order complete      234
Order continuity      239 286 287
Order continuous norm      241
Order interval      235
Order unit      238
Ordered Banach space      234 295
Ordered vector space      234
Ordinary differential equation      152 197 219
p-contractive operator      48
p-dissipative      48 128
p-dissipative operator      48 128
p-periodic      113
p-periodic forcing term      113
p-periodic solution of a Cauchy problem      113
Partial differential equation      26
Partially periodic semigroup      352 416
Periodic forcing term      116
Periodic semigroup      10 79 85 313 416
Periodic translation semigroup      66
Perron — Frobenius theory      163 172 292 296 379
Perturbation by multiplication operators      179 183 188 274 279 307
Perturbation theorems      43
Phillip’s theorem      249
Point spectrum      64 394
Polar decomposition      380 392
Pole      67 72 76 209 305 315
Pole of order k      73 86 174 295 303
Population equation      229 344 354 364
Positive cone      51 234 369
Positive group      146 148 295 326
Positive minimum principle      125 133 253 268
Positive operator      120
Positive part      235
Positive pseudo-resolvent      299
Positive semigroup      123
Positive subeigenvector      261
Positivity      118 119 120 123 238 242 244 370
Preadjoint semigroup      414
Predual      369
Projection      72 209 343 410 423
Pseudo-resolvent      298 314 372 383 392 419
Quasi-compact      214 343
Quasi-compact semigroup      214 343
Quasi-interior point      238 306
Quotient semigroup      15 74
Range condition      53 146 249 270
Real Banach lattice      243
Recurrent projection      407
Reduced semigroup      374 407
Regular mapping      242 272 279
Regularity      242 272 279
Rescaled semigroup      14
Residual spectrum      64
Residue      67 72 309 395
Resolvent      6 63 370
Resolvent equation      127 298
Resolvent integral representation      6 293
Resolvent positive      127
Resolvent positive operator      127
Resolvent pseudo      127
Resolvent set      63 75
Retarded Cauchy problem      219 356
Retarded differential equation      134 142 179 219
Retarded equation      356
Riesz Decomposition theorem      237
Riesz Schauder theory      72
Rotation group      10 69 352
Rotation semigroup      10 69 189 313 352
Schrodinger operator      179 273 278 336
Schwartz space      12 250
Schwarz inequality      370
Schwarz map      370 379 381 407
Second order derivative      11 34 179 185 249 308
Self-adjoint part      369
Semi flow      143 328
Semiflow      143 328
Semigroup      1
Semigroup dual      16
Semigroup of Schwarz type      370 379 408 424
Semigroup projection      209 310 343 411
Seperately continuous flow      149
Signum      137 256 276 296
Signum operator      170 246 256 296
Similar semigroup      13
Simple eigenvalue      73 305 310 388
Simple pole      73 209 310 315
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