Debnath L., Mikusinski P. — Introduction to Hilbert Spaces with Applications :: Электронная библиотека попечительского совета мехмата МГУ

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Debnath L., Mikusinski P. — Introduction to Hilbert Spaces with Applications

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Название: Introduction to Hilbert Spaces with Applications

Авторы: Debnath L., Mikusinski P.

Аннотация:

The Second Edition of this successful text offers a systematic exposition of the basic ideas and results of Hilbert space theory and functional analysis. It includes a simple introduction to the Lebesgue integral and a new chapter on wavelets. The book provides the reader with revised examples and updated diverse applications to differential and integral equations with clear explanations of these methods as applied to optimization, variational and control problems, and problems in approximation theory, nonlinear instability, and bifurcation.

Язык:

Рубрика: Математика/Анализ/Функциональный анализ/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1990

Количество страниц: 509

Добавлена в каталог: 09.04.2005

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Предметный указатель

Solution, stable      461
Solution, unstable      461
Solution, weak      296
Space spanned by $\mathcal{A}$       10
Space, $H^m(\Omega)= W_2^m(\Omega)$       97
Space, $L^1(\matbb{R})$       45
Space,       6 89
Space,       89
Space, $L^2(\matbb{R})$       74
Space, $L^2(\matbb{R}^N)$       75
Space,       6
Space, $\matbb{C}^N$       5
Space, $\matbb{R}$       3
Space, $\mathcal{C}([a, b])$       89
Space, $\mathcal{C}_0(\matbb{R})$       95
Space, $\tilde{H}^m(\Omega)$       96
Space, Banach space      19
Space, C      3
Space, Euclidean      92
Space, finite dimensional vector space      10
Space, Hilbert      93
Space, infinite dimensional      10
Space, infinite sequence      6
Space, inner product      88
Space, non-separable Hilbert      125
Space, pre-Hilbert      88
Space, separable Hilbert      124
Space, Sobolev      96
Space, test function      285 294
Space, vector      4
Spectral theorem for self-adjoint compact operators      189
Spectral theorem for unbounded operators, Spectrum      177
Sphere      14
Spherical harmonics      377
Spherically symmetric potential      375
Spin      400
Square integrable functions      74 76
Square root of an operator      165
Stability criterion      463
Stable solution      461
Stampacchia      445
Standard deviation      359
State equation      452
State function      349 447
State transition matrix      449
State vector      347
States      345
Stationary point      425
Stationary state      362
Step function      38 75
Strictly convex norm      127
Strictly positive functional      143
Strictly positive operator      166
Strong convergence      25 97
Sturm — Liouville systems      257
subspace      5
Successive approximation      234
Summability kernel      113
Support      39
Symmetric bilinear functional      143
Symmetric operator      206
Synthesis of a pulse      271
Tautochronous motion      247
Telegrapher equation      299
Tent function      83

Test function space      285
Theorem, Banach fixed point      30
Theorem, closed graph      208
Theorem, compatibility      407
Theorem, contraction mapping      30 225
Theorem, convolution      196
Theorem, Ehrenfest      375 383
Theorem, Fubini’s      78
Theorem, Hilbert — Schmidt      187
Theorem, implicit function      470
Theorem, Lax — Milgram      148
Theorem, Lebesgue dominated convergence      60
Theorem, Lions — Stampacchia      445
Theorem, Lyapounov      463
Theorem, mean value      415
Theorem, monotone convergence      59
Theorem, orthogonal projection      120
Theorem, Picard existence      228
Theorem, Plancherel      202
Theorem, Riesz representation      123
Theorem, Spectral      189 211
Theorem, virial      408
Theorem, Weierstrass approximation      17
Time-dependent Schrodinger equation      363
Time-dependent state vector      347
Time-evolution equation      381
Time-evolution operator      379
Time-invariant      447
Total angular momentum      403
Total energy      335 353
Total Hamilton operator      389
Transfer function      271
Transition matrix      449
Triangle inequality      11 91
Trigonometric Fourier series      112
Two-sided shift operator      214
Unbounded operators      203
Uncertainity      359
Uncertainty principle      360
Uniform convergence      12 25
Unitary operator      160
Unitary space      88
Universal constant      346
Unstable solution      461
Variables      345
Variational inequalities      443
Variational problems      311 411
Vector space      4
Vector subspace      5
Virial theorem      408
Volterra equation      236 246
Volterra equation of the first kind      223 246
Volterra equation of the second kind      224 237
Vorticity transport equation      322
Walsh functions      111
Wave equation      299 300 318
Wave function      349
Wave-particle duality      370
Weak convergence      97
Weak distributional convergence      289
Weak solution      296 311
Weierstrass approximation theorem      17
Weight function      253
Weighted average      357
wronskian      260
Zeeman effect      400

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