Reed M., Simon B. — Methods of Modern mathematical physics (vol. 2) Fourier analysis, self-adjointness :: Электронная библиотека попечительского совета мехмата МГУ

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Reed M., Simon B. — Methods of Modern mathematical physics (vol. 2) Fourier analysis, self-adjointness

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Название: Methods of Modern mathematical physics (vol. 2) Fourier analysis, self-adjointness

Авторы: Reed M., Simon B.

Аннотация:

This volume will serve several purposes: to provide an introduction for graduate students not previously acquainted with the material, to serve as a reference for mathematical physicists already working in the field, and to provide an introduction to various advanced topics which are difficult to understand in the literature. Not all the techniques and application are treated in the same depth. In general, we give a very thorough discussion of the mathematical techniques and applications in quatum mechanics, but provide only an introduction to the problems arising in quantum field theory, classical mechanics, and partial differential equations. Finally, some of the material developed in this volume will not find applications until Volume III. For all these reasons, this volume contains a great variety of subject matter. To help the reader select which material is important for him, we have provided a "Reader's Guide" at the end of each chapter.

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Рубрика: Математика/Математическая Физика/Учебники/

Статус предметного указателя: Готов указатель с номерами страниц

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Год издания: 1975

Количество страниц: 370

Добавлена в каталог: 24.04.2005

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Предметный указатель

$C^{\alpha}$ -vector      201
$L^{P}$ inequalities      32
$L^{P}$ -contractive semigroup      255
A-bounded      162
A-closed      138
A-compact      340
A-orthogonal      138
A-symmetric      138
Absolute value of an operator      196
Absolutely continuous subspace      230
Accretive operator      240
action      275
Adjoint, Banach space      185
Adjoint, Hilbert space      186
Adjoint, unbounded operator      252
Almost completeness      338
Analytic Fredholm theorem      201
Analytic function, vector-valued      189—190
Analytic vector      201
Anharmonic oscillator      17 184 206 266 270
Annihilation operator      142 208 217 218 219
Antilinear operator      69
Approximate identity      251 9
Approximate symbol      98
Ascoli’s Theorem      30
Asymptotic symbol      98
Atomic model      304
Axiomatic quantum field theory      62
B.L.T. theorem      9
Baire category theorem      80
Baire measure      105 110
Banach — Alaoglu theorem      115
Bessel’s inequality      38
Bochner integral      119
Bochner — Schwartz theorem      14
Bochner’s theorem      13
Boson Fock space      53
Boundary value      19
Bounded holomorphic semigroup      248
Bounded operator      8
Bros — Epstein — Glaser lemma      21
Canonical commutation relations      274 218 232
Canonical conjugate momentum      215
Canonical form for compact operators      203
Canonical free field      215
Cauchy principal value      136
Closable operator      250 252—253
Closed graph theorem      83
Closed operator      250
Closed quadratic form      277
Closure      92
Closure of an operator      250
Commuting (unbounded) operators      271—272
Compact operator      199
Compact support, distributions      139 178 17
Compact support, functions      111
Complete, classically      148
Complete, quantum mechanically      155
Completely continuous operator      (see “Compact operator”)
Cone      109 19
Cone, dual      19
Conjugation      143
Consistent norms      35
Continuous functional calculus      222
Contraction mapping theorem      151
Contraction mapping theorem, semigroup      235
Convex cone      109
Convex set      109
Convolution distributions      7
Convolution distributions, functions      6
Core      256
Coulomb gauge condition      190
Creation operator      142 204 209 217—219
Cyclic vector      226
Cyclicity of the vacuum      65
Davies — Faris theorem      186
Deficiency indices      138
Deficiency subspace      138
Densely bounded      272
Dirac operator      326 337
Distributions compact support      139 178 17
Domain      2
Dominated Convergence Theorem      17 24
Dual cone      19
Dunford functional calculus      245
Dunford — Taylor formula      316
Dyson expansion      282E
Elliptic operator      112
Elliptic regularity      49
Energy operator      (see “Hamiltonian”)
Equivalent representations      231
Essential range      229
Essentially self-adjoint      256
Extended forward tube      68
Extension of an operator      250
Faris — Lavine theorem      199
Fermion Fock space      54
Feynman — Kac formula      279
Finite particle vector      208
Finite propagation speed      309—310
First resolvent formula      191
Fock space      53
Form core      277
Form domain      276
Form domain of operator      277
Forward      66
Forward tube      66
Fourier inversion theorem      3
Fourier transform      1
Frechet space      132
Free field      212 215 217 223
Free Green’s function      59
Free Hamiltonian mass m (quantum field theory)      220
Free propagator      60
Friedrichs extension      177
Functional calculus      222 225 245 263 286—287
Functions of rapid decrease      133
Fundamental solution      46
Garding — Wightman axioms      61—65
Gauge condition      190
Generalized convergence      (see “Norm resolvent sense” “Strong
Generalized function      148
Generator group      268
Generator group, semigroup      237 246
Graph      83 250
Graph limits      293—294 268
Green’s functions      59
Hadamard’s three line theorem      33
Hahn — Banach theorem      75—77 130
Hamburger moment problem existence      145
Hamburger moment problem existence, uniqueness      205
Hamiltonian      303
Hamiltonian, free      55 220
Hamiltonian, time dependent      109
Hardy — Lebesgue class      109
Hausdorff — Young inequality      11
Heat equation      242 243 245 254
Hermite functions      142
Hermite functions, completeness      121
Hermitian operator      (see “Symmetric operator”)
Hermitian scalar quantum field theory      62 212
Hilbert — Schmidt operators      210—211
Hilbert — Schmidt theorem      203
Hille — Yosida theorem      238
Hille — Yosida — Phillips theorem      247
Hoelder continuous      81
Hoelder inequality      68 34
Holomorphic semigroup      252
Holomorphic semigroup, bounded      248
Hunt's interpolation theorem      31

Hypercontractive semigroup      258
Hypersurface      78
Hypoelliptic      112
Inequalities      32
Infinitesimal generator, group      268
Infinitesimal generator, semigroup      237 246
Infinitesimally small form      168
Infinitesimally small operator      162
Interaction representation      283
Interpolation, norms      37
Interpolation, spaces      37
Interpolation, theorem, Calder — Lions      37
Interpolation, theorem, Hunt      31
Interpolation, theorem, Marcinkievvicz      31
Interpolation, theorem, Stein      40
Inverse Fourier transform      1
Irreducible      232
Jost points      68
Kalf — Walter — Schmincke — Simon theorem      186
Kallen — Lehmann representation      70
Kato — Rellich theorem      162
Kato — Rellich theorem, symmetric form      163
Kato’s inequality      183
Kato’s theorem      166
Klein — Gordon equation      293
KLMN theorem      167
Konrady’s trick      175
Light cone      63
Limit circle      1
Limit point      1
Liouville form      314
Liouville operator      314
Liouville’s theorem      315
Lipschitz      154
Local commutativity      65
Local Sobolev space      51
Lorentz group      63
Lorentz invariant inner product      63
Lorentz invariant inner product, measures      74
m-accretive      168 240
Magnetic field      173
Magnetic vector potential      173
Malgrange — Ehrenpreis theorem      48
Manifold stationary phase      101
Manifold stationary phase, Symplectic      337
Marcinkiewicz interpolation theorem      31
Mass hyperboloids      70
Mathieu equation      320
Maximal accretive operator      240
Maximal interval of existence      301
Maximal symmetric operator      141
Microscopic causality      65
Moments of a measure      145
Momentum operators      304 65
Monotone Convergence Theorem      17 24
Monotone convergence theorem for nets      106
Multiplicity free operators      231
Multiplicity theory      231—234
n-particle subspace      208
n-point function      66
Nelson’s analytic vector theorem      202
Nelson’s commutator theorem      193
nonrelativistic quantum mechanics      15
Norm resolvent sense, convergence in      284—291
Normal bundle      120
Normal operator      246
Normalized tangent functional      240
Norms consistent      35
Norms consistent, interpolating      37
Nuclear theorem      141 144
Number operator      142 204 208 220
Nussbaum’s lemma      201
of an unbounded operator      249
One-parameter unitary group      265
Open mapping theorem      82 132
Operator positively preserving      186
Operator positively preserving, relatively bounded      162
Operator positively preserving, self-adjoint      187 255
Operator positively preserving, symmetric      255 192
Oscillatory integral      100
Paley — Wiener theorems      16 17 18 23 109
Parallelogram law      38 63
Parseval’s relation      45 46
Partial isometry      197
PCT theorem      69
Phase function      99
Phase space      313
Plancherel theorem      10
Poincare group      63
Poincare Invariance      65
Poisson bracket      314
Polarization identity      63
Positive distribution      162
Positive linear functional      106
Positive operator      195
Positive quadratic form      276
Positive type distribution      14
Positive type distribution, function      12
Positive type distribution, weak      14
Positivity preserving operator      186
Principle of uniform boundedness      81 132
Product formula      295—297 245
Product of distributions      90
Product topology      94
Projection      187
Projection theorem      42
Projection valued measure      234—235 262—263
Projection, orthogonal      187
Propagator      60 282
Pseudo-differential operator      119
q-space      228
Quadratic form      276
Quantum field      64 (see also “Free field and Canonical free field”)
Quantum field theory      62
quantum mechanics      302—305
Quasi-analytic vector      327
Radon — Nikodym theorem      25
Reconstruction theorem      114
Regular directed point      92
Regular point      88
Regularity of the field      64
Regularity, Schroedinger's equation      54
Regularity, tempered distributions      139 144
Regularity, theorem (Weyl’s lemma)      53
Regularly imbedded submanifold of codimension k      78
Relatively bounded form      168
Relatively bounded operator      162
Relatively compact      340
Relativistic invariance      62
Resolvent      188 253
Resolvent set      188 253
Restricted Lorentz group      63
Restricted Poincare group      63
Riemann — Lebesgue lemma      10
Riesz lemma      43 41—44
Riesz — Fischer theorem      18 24 68
Riesz — Thorin theorem      27
Rigged Hilbert space      44
Rollnik potential      170
Scalar quantum field theory      62 212
Scale of spaces      278 44
Schrodinger equation      303
Schrodinger representation      274
Schwartz space      133
Schwarz inequality      38
Schwinger functions      114
Second quantization      302 308 208
Segal field operator      209
Segal quantization      209
Self-adjoint operator bounded      187

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