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Zeidler E. — Applied Functional Analysis: Applications to Mathematical Physics
Zeidler E. — Applied Functional Analysis: Applications to Mathematical Physics



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Название: Applied Functional Analysis: Applications to Mathematical Physics

Автор: Zeidler E.

Аннотация:

This is a incredible book on applied functional analyses. Every topic is motivated with an applied problem. The definitions are motivated either by the aplication or by the subsequent use. There are remainders showing you the inteconections between the subjects and finally the index and the Symbols index are both complete and very usefull. The book is not complete. However he missing subjects usually are in the other colection by the same author.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1995

Количество страниц: 509

Добавлена в каталог: 04.02.2014

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Generalized plane wave      184
Generalized problem      285 306 310
Generalized solution      258
Generalized triangle inequality      8
Generator      298
Geometric series      79
Golden rule for the rate of convergence      143
Golden rule of numerical analysis      143
Graph      414
Graph closed operators      414
Green function      147 157 164 246 251 387 392
Group property      300
Half-numberly spin      357
Hamiltonian      328 371 418
Hamiltonian of the harmonic oscillator      341
Hamiltonian of the hydrogen atom      420
Harmonic oscillation in quantum mechanics      338
Harmonic oscillations      196 303
Heat equation      182
Heisenberg S-operator      402
Heisenberg uncertainty principle      331 342
Hermitean functions      210 339
Hermitean polynomials      210
Hilbert space      107
Hilbert — Schmidt operator      347
Hilbert — Schmidt theory      232
Hoelder continuous functions      96 97
Homeomorphic      28
Homeomorphism      28
Homogeneity in time      302
Hydrogen atom and the Friedrichs extension      420
I (or id), identical operator, Ix:=x for all x      76
Idea of orthogonality      124
Ideal elements      127
Identical operator      77
Infinite series      76
Infinite-dimensional space      6
Initial-value problem      24
Injective      17
Inner product      105
int S, interior of the set S      31
Integer spin      357
Integrable      434
Integral equations      22 62 240
Integral of a step function      432
Integral operator      18 40 265
Integration by parts      117 119 159
Interior      31
Interior point      31
Inverse Fourier transformation      216 378
Inverse operator      17
Inverse scattering theory      406 409
Irreversible process in nature      300 303
Isometric operators      422
Iterated integration      438
Iteration method      18 68 395 404
k-contractive      19
Kato perturbation theorem      417
KdV equation      407
kinetic energy      321 336
KMS-states      360
Knaster, Kuratowski, and Mazurkiewicz lemma      58
Korteweg — de Vries equation      406
L(X, Y), $L_{inv}(X, Y)$, spaces of continuous functions      73 79
Lack of classic solution      127
Lagrange multiplier rule      354
Laguerre functions      222
Language of physicists      221 373
Laplacian      125 277 285
Lax pair      412
Lax — Milgram Theorem      174
Least-squares method      201
Lebesgue integral      434
Lebesgue measure      429
Lebesgue spaces      114
Lebesgue — Stieltjes integral      441
Legendre polynomials      209
Leray — Schauder principle      64
Linear combinations      2
Linear continuous functional      74
Linear hull      31
Linear integral equation      23
Linear Lax — Milgram theorem      175
Linear operator      70
Linear orthogonality principle      172
Linear space      3
Linear subspace      30
Linearly independent      5
Lipman — Schwinger integral equation      404
Lipschitz continuous      27
Luzin's theorem      432
Majorant criterion      436
Malgrange — Ehrenpreis theorem      186
Mapping degree      55
Mass conservation      379
Matrix      71
Maximally skew-symmetric      267
Maximally symmetric      267
Maximum      37
Maxwell — Boltzmann statistics      356
Mean continuity      437
meas S, measure of the set S      431
Measurable functions      432
Measurable set      430
Measure      430
Measurements      328 349
Method of finite elements      145
Microscattering processes      400
Mild (generalized) solution      307 311 320 324
Minimal sequence      176
Minimum      37
Minkowski functional      50
Mixed state      358
Models of quantum field theory      368
Momentum operator      342 345 376
Momentum vector      336
Monotone convergence      437
Monotone operators      173
Multiindex      159
Multiplication operator      269 334
Multiplicity      230
N(A) (or ker A), null space (or kernel) of the operator A, N(A):={x:Ax = 0}      70
Navier — Stokes equations      65
Neighborhood      15
Neumann series      79
Newtonian equation      336
Nonexpansive semigroup      299
Nonlinear Fourier transformation      413
Nonlinear Lax — Milgram theorem      175
Nonlinear mathematical physics      173
Nonlinear orthogonality principle      174
Norm      7
Normal order cone      67
Normed space      7
Nuclear spaces      424
Null space      70
Observables      328 359
One-dimensional wave      323
One-parameter group      299
One-parameter unitary group      301 328
open      15
Open neighborhood      15
Operator      16
operator functions      76 77 257
Operator norm      70
Order cone      66
Ordered Banach space      67
Ordered normed space      67
Ordered sets      441
Ordinary differential equations      24 63
Orthogonal      105
Orthogonal complement      165 178
Orthogonal decomposition      165
Orthogonal projection      165 270
Orthogonality      124
Orthogonality principle      172 175
Orthonormal system      199
Parallelogram identity      123 178
Parameter integrals      439
Parseval equation      203 222
Partial differential equations of mathematical physics      256
Particle number      352
Particle number operator      366
Particle stream      344 403
Partition function      353
path integral      390
Pauli principle      356 363
Payley — Wiener theorem      186 223
Peano theorem      63
Perpendicular principle      123 165
Phase space      393
Photon      340
Physical interpretation of the Green function      158
Physical states      327
Picard — Lindeloef theorem      24
Planck quantum action      329
Planck's radiation law      340 357
Plane wave      184
Poincare inequality      287
Poincare — Friedrichs inequality      136
Poisson equation      125 258 285
Position operator      342 346 377
Positive bilinear form      120
Potential      182
Potential barrier      403
potential energy      321 336
Potential equation      182
Potential theory      95
Pre-Hilbert space      105
Preimage      17
Principle of indistinguishability      363
Principle of maximal entropy      353
Principle of minimal potential energy      256
Principle of minimal potential errors      142
Principle of stationary action      321
Principle of virtual power      142 147
Principle of virtual work      147
probability      336 352
Probability conservation of quantum processes      303
Probability of measuring the position      343
Product rule      107
Propagation of probability      393
Propagator      387
Pure state      358
Pythagorean Theorem      167
Quadratic variational problems      121
Quantization      336
Quantization of action      393
Quantum field theory      363
Quantum hypothesis      340
quantum mechanics      327 336
Quantum statistics      348
Quantum system      327
R(A) (or im A), range (or image) of the operator A      17
r(A), spectral radius of the linear operator A      94
RANGE      17
Rate of convergence      19 142
Real linear space      4
Real normed space      7
Regularity theory      128
Relatively compact      90
Relatively sequentially compact      33
Rellich's compactness theorem      287
Resolvent      83
Resolvent set      83
Resonance condition      249
Restriction      259
Retraction      55
Reversibility      302
Reversible processes in nature      302
Riesz theorem      167
Ritz equation      140 152
Ritz method      140 151 179
S+T, the sum $S+T:=\{x+y:x\in S and y\in T\}$      7
S-matrix      402
Scalar multiplication      3
Scattering of a particle stream      399
Scattering theory      368
Schauder fixed-point theorem      61
Schauder operator      41
Schmidt orthogonalization method      207
Schroedinger equation      323 336 338 381 395
Schwarz inequality      105
Self-adjoint operator      264 416
Semi-Fredholm      83
Semigroup      298
Separability      191
Separable      84 116
Sequentially compact      33
Sequentially continuous      27
Sharp energy      341
Simple eigenvalue      247
simplex      46
Skew-adjoint operator      264
Skew-symmetric operator      264
Smoothing of functions      186
Smoothing technique      117
Sobolev Embedding Theorems      192
Sobolev space      130 260 277
Solitons      406
span S, linear hull of the set S      31
Spectral family      333
Spectral radius      94
Spectral transformation      410
Spectrum      83 94 238
Spectrum of the hydrogen atom      421
Sperner Lemma      56
Sperner simplex      57
Standard model in statistical physics      351 360
States      327 359
Stationary particle states      337
Stationary Schroedinger equation      337
Statistical operator      350
Statistical potential      353
Statistical states      348
Step function      432
Stieltjes integral      333 440
String      158 315
String energy      320
String equation      321
Strong causality      302
Strongly continuous semigroup      298
Strongly monotone operators      173 259 273
Strongly positive bilinear form      120
Subsolution      69
Superposition      196
Superposition of eigenoscillations      317
Superselection rules      328
Supersolution      69
Surjective      17
Symmetric bilinear form      120
Symmetric operator      230 264 415
Tempered delta distribution      221
Tempered distributions      220
Tensor product      224 226
Tensor product of functions      184
Tensor product of generalized functions      185
Theorem 1.A, the Banach fixed-point theorem      19
Theorem 1.B, the Brouwer fixed-point theorem      53
Theorem 1.C, the Schauder fixed-point theorem      61
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