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Pastur L., Figotin A. — Spectra of Random and Almost-Periodic Operators
Pastur  L., Figotin A. — Spectra of Random and Almost-Periodic Operators

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Название: Spectra of Random and Almost-Periodic Operators

Авторы: Pastur L., Figotin A.

Аннотация:

The study of the spectra and related characteristics of random and almost periodic operators of various types (Schrödinger, continuous, discrete and more general) is a lively and fascinating field of research lying at the intersection of mathematical physics, spectral theory of operators and probability theory. A widespread interest in the domain and a vast amount of mathematical activity have led to many remarkable new results and viewpoints yielding insight even into traditional questions. This book by two of the leading researchers having contributed to this field is the first systematic treatment of the fundamental problems and the large body of mathematical results known, and thus fills the gap in the reference literature. Not content to highlight the important ideas and recently developed concepts and methods, it also provides a large number of exercises illustrating these, to guide the reader towards improvements and generalizations. This long-awaited book is a welcome addition to the literature both for specialists in the field and for graduate students moving into research, as well as for all interested in the major problems of mathematical physics today.


Язык: en

Рубрика: Математика/Анализ/Функциональный анализ/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1992

Количество страниц: 586

Добавлена в каталог: 14.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$(\delta,\lambda)$-regular      390
Absolutely continuous      41
Admissible potential      119
Allowed bands      119 420
Almost periodic function      30
Almost-Mathieu Operator      460
Amplitude of the Cauchy solution      257
Anderson localization      379
Anderson model      15
Attraction      386
Band structure      119 420
Bernoulli potential      165
Besicovitch norm      472
Bicrystal model      375
Block resolvent expansion      392
Bohr almost periodic function      31
bonds      123
Bragg points      430
Brillouin zone      119
Brownian Motion Model      157
Cauchy distribution      130
Cauchy problem      137
Characteristic functional      32
Cocycle (Lyapunov) spectrum      263
Complete regularity      20
Completely nondeterministic      20
Components, homogeneous      307
Concentrated (measure)      546
Condition $\Phi$      529
Consistency conditions      10
Continuous spectrum      41
Cumulative      60
Cylinder      11
Deterministic      20
Dichotomous process      25
Diophantine condition      431 506
Direct problem      454
Discrete spectrum      41
distribution      10
Duality      461
Eigenfunctions and eigenvalues, generalized      397
Ergodicity      18
Essential closure      306
Essential spectrum      41
Events      9
Exponential decay      318
Exponential localization      379
Feller process      153
Feynman — Kac formula      100
Finite-band potential      119 421
Floquet — Bloch solutions      420
Fluctuation boundaries      146 198
Fokker — Planck — Kolmogorov equation      54 154
Forbidden bands      119 420
Fundamental matrix      259
gaps      119 420
Gaussian process      12
Gaussian random field      26
Generalized eigenfunctions and eigenvalues      397
Generalized Poisson measure      29
Generalized Poisson random field      30
Generating subspace      47
Glivenko — Cantelli theorem      60
Green function      169 290 293
Herbert — Jones — Thouless formulas      275
Herglotz functions      293
Hill discriminant      132 420
Hoelder condition      166
Homogeneous components      307
Homogeneous Markov process      23
Homogeneous random field      17—18
Homological equation      507
Homological matrix      454
Hull      31
Infinitesimal operator      154
Integrated density of states      60—61
Interaction, absence of      386
Invariant distributions      151
Invariant random variable      22
Jacobi matrix      14
Joint distribution      10
Kolmogorov — Chapman — Smoluchowski equation      153
Kolmogorov — Fokker — Planck equation      54 154
Kronig — Penny model      172
Lacuna      420
Laplace characteristic functional      32
Laplace — Beltrami operator      157
Lifshitz exponent      218
Limit spectrum      41
Limit-periodic potential      464
Liouville number      461
Local perturbation      324
Local time      226
Localization radius      381
log-Hoelder function      165
Lyapunov characteristic exponents      258
Lyapunov cocycle spectrum      263
Lyapunov exponent      262
Lyapunov function      420
Markov chain      26
Markov random process      23
Mathematical expectation      9
Maximally homogeneous      307
Metrically transitive automorphism      21
Metrically transitive group      21
Metrically transitive operator      33
Metrically transitive random field      18
Mixing      19
Mobility edge      528
Module (of almost-periodic function)      422
Morse function      157
Multidimensional Schroedinger operator      15
Multiplicative cocycle      260
Multiplicative ergodic theorem      263
Nevanlinna function      292 546
Nondeterministic random field      20
Nonflat function      157
Nonrandom      36
Ornstein — Uhlenbeck process      26 55
Oscillation theorem      140
Phase      137
Phase, reduced      149 345
Point spectrum      41
Poisson random field and measure      27
Polynomially bounded      318
Probability measure and space      9
Pure point spectrum      41
Purely continuous      41
Quasimomentum      420
Quasiperiodic potential      430
Random field      11
Random function      10
Random operator      13
Random process      11
Random projection      16
Random telegraph signal      25
Random variable      9
Random vector      13
Randomizing parameters      323
Rationally independent      31
Realization      9
Reduced phase      149 345
Regular random field      20
Repulsion      386
Resolution of the identity      39
Resonance tunneling      318
Reversible process      56
Rice — Kac formula      156
Schroedinger operator      14
Separable random function      13
Singular continuous      41
Singular random field      20
Slowly varying potential      285
Special energies (frequencies)      171
Spectral measure      291 294 396
Spectral multiplicity      47
Spectrum      41
Stability intervals      420
Stable boundary      145 191
Stationary random field      17
Stepanov functions      468
Stieltjes transform      544
Stochastically continuous      21 153
Stochastically equivalent      13
Strongly mixing      19
Sturm — Liouville operator      14
Subadditive ergodic theorem      138
Subharmonic      265
Substitution alloy      28 118
Support of a measure      46 310
Symmetric random operator      13
Tail algebra      20
Telegraph signal      25
Topological support      46 310
Transfer matrix      259
Uniform almost-periodic      31
Weyl functions      292
Weyl — Courant inequalities      110
White noise      173
Zero-one law      19
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