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

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

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$L^1$-norm      51
$L^2$ -norm      75
Abel’s formula      260
Abel’s integral equation      247
Abel’s problem      432
Absolutely convergent series      21
Abstract minimization problem      443
action      367
Adjoint boundary conditions      251
adjoint of a differential operator      250
Adjoint operator      149 204
Admissible set      425
Admittance      269
angular momentum      344 353
Angular momentum operator      396 400
Annihilation operator      392
Anomalous Zeeman effect      400
Anti-derivative of a distribution      293
Anti-Hermitian operator      155
Anti-linear functional      124
Appolonius’ identity      128
Approximate eigenvalue      186
Approximation theory      453
Associated Legendre functions      254 376
Associated Legendre operator      254
Asymptotically stable solution      461
Atomic units      372
Autonomous dynamical system      461
Banach fixed point theorem      30
Banach space      19
Basic representation      38
Basis      10
Beppo Levi      59
Bessel functions      256
Bessel operator      256
Bessel’s equality and inequality      104
Best approximation      453
Bifurcation      465
Bifurcation, diagram      466 468 470
Bifurcation, points      466
Biharmonic equation      300 323
Bilinear concomitant      251
Bilinear functional      143
Born      367
Bosons      402
Bounded bilinear functional      143
Bounded linear mapping      24
Bounded operator      138
Bounded quadratic form      144
Cartesian product      8
Cartesian product of vector spaces      8
Cauchy sequence      18
Cayley transform      213
Chain rule      419
Change of variable theorem      66
Characteristic function      38
Chebyshev operator      254
Chebyshev polynomials      131 254 460
Classical quantities      353
Classical solution      295
Closed balls      14
Closed graph theorem      208
Closed operator      208
Closed set      15
Closed unbounded operator      208
Closest point property      118
Closure      16
Coercive functionals      147
Commutation relations      354
Commutator      350
Commuting operators      141
Compact operator      171
Compact sets      17
Compact-normal resolvent      212
Compatibility theorem      407
Compatible observables      351
Complementary observables      351
Complementary projection operator      168
Complete normed space      19
Complete sequence      107
Completely continuous operator      171 176
Completion of a normed space      28
Complex vector space      4
Conjugate variables      339
Conjugate-linear functional      124
Conservation law of energy      384
Conservative      334
Constant of motion      335 387
Continuity equation      366
Continuous mapping      24
Continuous spectrum      177
Contraction      30
Contraction mapping      30
Contraction mapping theorem      30 225
Control function      447
Convergence in norm      53
Convergence in normed space      12
Convergence of test function      286
Convergence, absolute      21
Convergence, almost everywhere      55
Convergence, pointwise      12
Convergence, strong      25 97
Convergence, uniform      12 25
Convergence, weak      97
Convergence, weak distributional      289
Convex functions      423
Convex sets      118
Convolution      79
Convolution theorem      196
Correspondence principle      353
Cost functional      447
Creation operator      392
de Broglie wave      370
Degenerate eigenvalue      178
Degree of degeneracy      178
Dense subsets      17
Densely defined operator      204
Derivative, Frechet      416
Derivative, Gateaux      412
Derivative, second Frechet      420
Derivatives of distributions      288
Differential operator      139
Diffusion equation      299 316
DIMENSION      10 348
Dirac delta distribution      288
Dirichlet integral      303
Dirichlet problem      310
dispersion relation      368
Distributional solution      296
Distributions      287 294
Domain      23
Domain of a differential operator      250
Dual space      27
d’Alembert solution      318
Ehrenfest’s theorem      375 383
Eigenfunction      176 253
Eigenvalue      176 253
Eigenvalue space      178
Eigenvector      176
Elliptic functional      147
Elliptic operator      310
Equality almost everywhere      54
Equation of continuity      366
Equation, Abel integral      247
Equation, Bessel      256
Equation, biharmonic      300 323
Equation, continuity      366
Equation, diffusion      299
Equation, Euler — Lagrange      428 430 435
Equation, Fredholm integral      224 232 233
Equation, Hamilton      340
Equation, Hamilton — Jacobi      367
Equation, Heisenberg      386
Equation, Helmholtz      299 300 310
Equation, Hermite      257
Equation, homogeneous integral      224
Equation, integral      223
Equation, Klein — Gordon      300
Equation, Lagrange      336 338 431
Equation, Laguerre      255
Equation, Laplace      298 319 320
Equation, Legendre      254
Equation, matrix Riccati differential      451
Equation, Navier — Stokes      322
Equation, Newton      334
Equation, non-homogeneous integral      224
Equation, non-homogeneous wave      299
Equation, nonlinear Fredholm integral      233
Equation, ordinary differential      248 268
Equation, partial differential      295
Equation, Poisson      299 305
Equation, Schrodinger      300 362 375
Equation, state      452
Equation, Sturm — Liouville      257
Equation, telegrapher      299
Equation, Volterra integral      223 224 236 237 239 246
Equation, vorticity transport      322
Equation, wave      299 300
Equations of motion      345
Equilibrium solution      461
Equivalence of norms      13
Euclidean norm      11
Euclidean space      92
Euler — Lagrange equations      428 431 435 436 439
Existence and uniqueness of solution      228 229 232 233
expectation value      355
Extension of operators      204
Extremum      425
Fatou’s Lemma      61
Fejer’s kernel      114
Fermat’s principle      431
fermions      402
Finite dimensional operator      173
Finite dimensional vector space      10
Fixed point      29 224
Fixed point theorem      30
Formally self-adjoint differential operator      251
Fourier coefficients      117
Fourier series      117
Fourier transform      193 198
Frechet derivative      416
Fredholm alternative      229
Fredholm alternative for self-adjoint compact operators      229
Fredholm equations      224 232 233 274
Fredholm operator      151
Friedrich’s first inequality      311
Fubini’s Theorem      78
Function of an operator      191
Function spaces      5
Function, associated Legendre      254
Function, Bessel      256
Function, characteristic      38
Function, control      447
Function, convex      423
Function, Dirac delta      269 288
Function, eigen-      176 253
Function, Green’s      263 298
Function, Hamilton’s      339 431
Function, Hamilton’s principal      367
Function, Heaviside      288
Function, input      269
Function, Lagrangian      335
Function, Lebesgue integrable      43 75
Function, locally integrable complex valued      74
Function, measurable      70
Function, momentum density      372
Function, momentum wave      371
Function, null      52
Function, output      269
Function, Rademacher      110
Function, series of integrable      50
Function, smooth      285
Function, square integrable      74 76
Function, state      349 447
Function, step      38 75
Function, tent      83
Function, test      285
Function, transfer      271
Function, Walsh      111
Function, wave      349
Function, weight      253
Functional      27
Functional, anti-linear      124
Functional, bilinear      143
Functional, bounded bilinear      143
Functional, coercive      147
Functional, conjugate linear      124
Functional, cost      447
Functional, elliptic      147
Functional, linear      27
Functional, positive bilinear      143
Functional, quadratic      441
Functional, sesquilinear      143
Functional, strictly positive      143
Functional, symmetric bilinear      143
Fundamental matrix      448
Fundamental solution      297
Gateaux derivative      412
Gegenbauer polynomials      132
Generalized coordinates      336
Generalized force      339
Generalized Fourier coefficients      106
Generalized Fourier series      106
Generalized momentum      339
Generator      345 380
Geodesic      437
Gradient      418
Gradient of a functional      413
Gram — Schmidt orthonormalization process      56
Graph      23 208
Graph of an operator      23 208
Green’s first identity      301
Green’s function      263 298
Green’s second identity      301
Ground state energy      392 393
Group velocity      369
Hamilton — Jacobi’s equation      367
Hamiltonian      339 353 431
Hamiltonian operator      362
Hamilton’s canonical equation      340 386
Hamilton’s function      339 431
Hamilton’s principal function      367
Hamilton’s variational principle      342
Hammerstein operator      418
Heaviside function      288
Heisenberg commutation relation      351 354
Heisenberg operator      385
Heisenberg picture      378 384
Heisenberg’s equation of motion      385
Heisenberg’s uncertainty principle      359
Helmholtz equation      299 300 306 308
Hermite operator      256
Hermite polynomials      102 256
Hermitian operator      150
hilbert      87
Hilbert space      93
Hilbert space isomorphism      126
Hilbert transform      275
Hilbert — Schmidt theorem      187
Holder’s Inequality      7
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