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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
Homogeneous Dirichlet problem      298
Homogeneous integral equation      224
Homogeneous Neumann problem      298
Homogeneous Volterra equation      239
Idempotent operator      167
Identity operator      138
Image      23
Implicit function theorem      470
Index of performance      447
Infinite dimensional vector space      10
Inner product      88
Inner product space      88
Input function      269
Integral equations      223
Integral of a step function      39
Integral operator      140
Integral over an interval      62
Interaction picture      378 389
Intrinsic angular momentum      400
Inverse differential operators      263
Inverse Fourier transform      201
Inverse image      23
Inverse operator      155
Invertible operator      155
Isometric operator      159
Iterated kernels      240
Jacobian matrix      414
Jacobi’s identity      404
Jacobi’s operator      255
Jacobi’s polynomials      132 255
Kernel      223
kinetic energy      334 353
Klein — Gordon equation      300
Lagrange identity      260
Lagrange’s equations of motion      336 431
Lagrangian      431
Lagrangian function      335
Laguerre operator      255
Laguerre polynomials      130 255
Laplace equation      298 319 320
Laplace operator      298 319 320
Law of conservation of energy      341
Lax      148
Lax — Milgram Theorem      148
Least — Square approximation      455
Lebesgue      37
Lebesgue dominated convergence theorem      60
Lebesgue integrable functions      43 75
Lebesgue integral      43
Lebesgue integral for complex valued functions      72
Lebesgue measure      68
Legendre equation      254 376
Legendre operator      254
Legendre polynomials      100 102 254 376
Linear combinations      9
Linear dependence      9
Linear functional      27
Linear harmonic oscillator      390 394
Linear independence      9
Linear mapping      23
Linear momentum      334 353
Linear operator      138
Linear transformation      138
Lions      445
Lions — Stampacchia theorem      445
Lipschitz’s condition      228 277
Locally integrable complex valued functions      74
Locally integrable functions      62 76
Lowest state energy      392
Lyapounov’s theorem      463
MacNeille      38
magnetic quantum number      337
Matrix Riccati equation      451
Maxwellian distribution      395
Mean value theorem      415
Measurable functions      70
Measurable sets      68
Measure      68
Measurement      349
Method of successive approximation      225 234
Mikusinski      38
Milgram      148
Minkowski’s inequality      8
Momentum density function      372
Momentum wave function      371
Monotone Convergence Theorem      59
Multiple eigenvalue      178
Multiplication operator      140
Multiplicity      178
Multiplier      140
Navier — Stokes equation      322
Neumann      87
Neumann problem      298
Neumann series      227
Newton’s equation      334
Newton’s second law of motion      334 388
Non-degenerate eigenvalue      178
Non-homogeneous equation      224
Non-homogeneous Volterra equation      240
Non-homogenous wave equation      299
Non-separable Hilbert space      125
Nonlinear Fredholm equation      233
Norm      10 51 90 91
Norm in inner product space      91
Norm of a bounded bilinear functional      143
Norm of a bounded quadratic form      144
Norm of uniform convergence      12
Norm, $L^1$      51
Norm, $L^2$      75
Norm, $L^p$      11
Norm, Euclidean      11
Norm, strictly convex      127
Norm, sup      138
Norm, uniform      12
Normal operator      158
Normed space      11
Null function      52
Null operator      138
Null set      54
Null space      23
Observable operators      350
Observables      345
Observation      349
One dimensional Schrodinger equation      394
One-sided shift operator      159
Open balls      14
Open sets      15
Operator      23 138
Operator, adjoint      149 204
Operator, adjoint of a densely defined      204
Operator, adjoint of a differential      250
Operator, angular momentum      396 400 403
Operator, annihilation      392
Operator, anti-Hermitian      155
Operator, associated Legendre      254
Operator, Bessel      256
Operator, bounded      138
Operator, Chebyshev      254
Operator, closed      208
Operator, closed unbounded      208
Operator, commuting      141
Operator, compact      171
Operator, complementary projection      168
Operator, completely continuous      171 176
Operator, creation      392
Operator, densely defined      204
Operator, differential      139
Operator, elliptic      310
Operator, finite dimensional      173
Operator, formally self-adjoint differential      251
Operator, Fredholm      151
Operator, Hamiltonian      362
Operator, Hammerstein      418
Operator, Heisenberg      385
Operator, Hermite      256
Operator, hermitian      150
Operator, idempotent      167
Operator, identity      138
Operator, integral      140
Operator, inverse      155
Operator, inverse differential      263
Operator, invertible      155
Operator, isometric      159
Operator, Jacobi      255
Operator, Laguerre      255
Operator, Laplace      298 319 320
Operator, Legendre      254
Operator, linear      138
Operator, linear harmonic oscillator      390 394
Operator, linear momentum      334 353
Operator, multiplication      140
Operator, normal      158
Operator, null      138
Operator, observable      350
Operator, one-sided shift      159
Operator, orbital angular momentum      396
Operator, orthogonality of a projection      169
Operator, positive      161
Operator, positive definite      166
Operator, projection      166
Operator, quantum      353
Operator, Schrodinger      385
Operator, self-adjoint      150 206
Operator, square root of a positive      165
Operator, strictly positive      166
Operator, symmetric      206
Operator, time-evolution      379
Operator, total Hamiltonian      389
Operator, two-sided shift      214
Operator, unbounded      203
Operator, unitary      160
Optimal control problems      447
Optimal error      454
Optimal solution      454
Optimal trajectory      448
Optimization problems      424
Orbital angular momentum operators      396
Orbital quantum number      377
Ordinary differential equations      248 268
Orthogonal complement      117
Orthogonal decomposition      121
Orthogonal projection      120
Orthogonal systems      99
Orthogonal vectors      92
Orthogonality of projection operators      169
Orthonormal basis      124
Orthonormal polynomials      458
Orthonormal sequence      99
Orthonormal systems      99
Outcome of quantum measurement      358
Output function      269
Parallelogram law      91
Parseval relation of Fourier transforms      199 201
Parseval’s formula      108
Partial differential equation      295
Particle momentum      369
Pauli’s spin matrices      398
Periodic boundary condition      249
Periodic Sturm — Liouville system      258
Picard’s existence theorem      228
Plancherel theorem      202
Planck      345
Planck’s constant      345
Planck’s simple harmonic oscillator      394
Point spectrum      177
Pointwise convergence      12
Poisson equation      299 305
Poisson’s bracket      343 386
Polarization identity      128 144
Pontrjagin maximum principle      448
POSITION      353
Positive bilinear functional      143
Positive definite operator      166
Positive operator      161
potential energy      334 353
Pre-Hilbert space      88
Principal quantum numbers      377
Principle of linearized stability      462
Principle of quantization      354
Principle of superposition      306
Probability current density      366
probability density      365
Probability flux      366
Product of two operators      141
Projection onto S      121
Projection operator      166
Proper subspace      5
Pythagorean formula      92 104
Quadratic form      143
Quadratic functional      441
Quantization      354
Quantum number      393
Quantum operators      353
Rademacher function      110
RANGE      23
Real vector space      4
Regular distribution      287
Regular points      177
Regular Sturm — Liouville systems      257
Reisz representation theorem      123
Relative extrema      425
Representer of a functional      124
Resolution of a pulse      271
Resolvent      177 235
Riemann integrable functions      64
Riemann integral      64
Riemann — Lebesgue lemma      195
Riesz      58 123
Robin problem      298
Rodrigues formula      377
Root-mean-square deviation      355 359
Scalars      3
Schrodinger picture      378
Schrodinger’s equation      300 362
Schwartz      283
Schwarz’s inequality      90
Second Frechet Derivative      420
Self-adjoint and formally self-adjoint differential operator      251
Self-adjoint operator      150 206
Separability      125
Separable Hilbert spaces      124
Separable kernel      242
Separable spaces      124
Separated boundary conditions      249
Sequence spaces      6
Series of integrable function      50
Sesquilinear functional      143
Set of measure zero      68
Simple eigenvalue      178
Singular distribution      287
Singular Sturm — Liouville system      257
Smooth function      285
Snell’s law      432
Sobolev      97
Sobolev space      96
Solution, asymptotically stable      461
Solution, bifurcation      466
Solution, classical      295
Solution, distributional      296
Solution, equilibrium      461
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