Reed M., Simon B. — Methods of Functional Analysis (in 4 volumes). Volume 1: Functional Analysis :: Электронная библиотека попечительского совета мехмата МГУ

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Reed M., Simon B. — Methods of Functional Analysis (in 4 volumes). Volume 1: Functional Analysis

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Название: Methods of Functional Analysis (in 4 volumes). Volume 1: Functional Analysis

Авторы: Reed M., Simon B.

Аннотация:

This book is the first of a multivolume series devoted to an exposition of functional analysis methods in modern mathematical physics. It describes the fundamental principles of functional analysis and is essentially self-contained, although there are occasional references to later volumes. We have included a few applications when we thought that they would provide motivation for the reader. Later volumes describe various advanced topics in functional analysis and give numerous applications in classical physics, modern physics, and partial differential equations.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 2nd edition

Год издания: 1980

Количество страниц: 400

Добавлена в каталог: 09.12.2008

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Предметный указатель

spaces      68 348-
, , ,       94
$\sigma$ -field      23
$\sigma$ -finite      23
$\sigma$ -ring      23
$\varepsilon/3$ argument      26—27
Absolute value of an operator      196
Absolutely continuous subspace      230
Absorbing      127
Adjoint of unbounded operator      252
Adjoint, Banach space      185
Adjoint, Hilbert space      186
Affine linear map      151
Almost everywhere (a.e., )      17
Analytic completion      336
Analytic Fredholm theorem      201
Analytic function, vector-valued      189—190
Approximate identity      251 326
Ascoli’s Theorem      30
Atomic model      304
B.L.T.theorem      9
Baire category theorem      80
Baire functions      105
Baire measure      105 110
Baire sets      105 110
Balanced      127
Banach space      67
Banach — Alaoglu theorem      115
Banach — Alaoglu theorem, applications      354- 363
Banach — Steinhaus principle      see “Principle of uniform boundedness”
Base for a topological space      91
Bergmann kernel      347
Bessel’s inequality      38
Bicontinuous      92
Bijective      2
Bipolar theorem      168
Bochner integral      119
Bochner-Schwartz theorem      331
Bochner’s theorem      330
Bochner’s tube theorem      337
Bolzano -Weierstrass theorem      98
Bore! function      15
Borelsets      14 105
Boson Fock space      53
Boundary      92
Bounded linear transformation      8
Bounded operator      8
Bounded set      165
Bounded variation      33
Brouwer fixed point theorem      364
Canonical form for compact operators      203
Cantor function      21
Cantor set      20
Cartesian product      1
Cauchy net      125
Cauchy principal value      136
Cauchy sequence      5
Chemoff’s theorem      377
Circled      127
Closable form      373
Closable operator      250 252—253
Closed graph theorem      83
Closed operator      250
Closed quadratic form      277
Closure      92
Closure of an operator      250
Cluster point      96
Commuting (unbounded) operators      271—272
Compact operator      199
Compact operator, applications      204—206 368—372
Compact space      98
Compact support, functions of      111
Completely continuous operator      see “Compact operator”
Completion      7 9
Cone      109
Connected      95
Continuity of the functional calculus      286—287
Continuous function      6 92
Continuous functional calculus      222
Contraction mapping theorem      151
Convex cone      109
Convex function      356
Convex function, strictly      389
Convex set      109
Convolution      323 324
Core      256
Countable, first      94
Countable, second      94
Cyclic vector      226
Degenerate tube theorem      338
Dense      6
Direct sum of Banach spaces      78
Direct sum of Hilbert spaces      40
Directed family of semi norms      126
Directed system      95
Dirichlet problem      204- 206
Dirichlet’s principle      362
distribution      see “Generalized function” “Tempered
Domain      2
Domain of an unbounded operator      249
Dominated Convergence Theorem      17 24
Dual space      43 72
Dunford functional calculus      245
Dunford — Taylor formula      316
Eigenvalue      188
Eigenvector      188
Equicontinuous      29 28—30
Equivalence relation      2
Equivalent family of seminorms      126
Ergodic      58
Ergodic theorem, Birkhoff      60
Ergodic theorem, von Neumann      57
Essential range      229
Essentially self-adjoint      256
Exaggeration      60 1—400
Extension of an operator      250
f.i.p.      98
Fatou’s Lemma      24
Fermion Fock space      54
Filter      352
First resolvent formula      191
Fock space      53
Form core      277
Form domain      276
Form domain, of operator      277
Fourier coefficients      46
Fourier inversion theorem      320
Fourier transform      318
Frechet space      132
Fredholm alternative      203
Fubini’s Theorem      25—26
Functional calculus      222 225 245 263 286—287
Functions of rapid decrease      133
Gauge      see “Minkowski functional”
Generalized convergence      see “Norm resol vent sense” “Strong
Generalized function      148
Generalized function, of compact support      334
Geodesic      361
Graph      83 250
Graph limit      293—294
Haar measure      155
Hahn — Banach theorem      75—77 130
Hartree equations      359
Hausdorff space      94
Hausdorff — Young inequality      328
Hellinger — Toeplitz theorem      84
Hermitian      see “Symmetric operator”
Hilbert space      39
Hilbert — Schmidt operators      210
Hilbert — Schmidt theorem      203

Holder’s Inequality      68 84 348
Holomorphy domain      336
Holomorphy envelope      336
Homeomorphism      92
Homology group      364
Implicit function theorem      366
Infinitely divisible      341
Injective      2
Inner product      36
Interior      92
Inverse Fourier transform      318
Inverse function theorem      367
Inverse mapping theorem      83
Isometric isomorphism      71
Isometry      7
Kakutani — Krein theorem      104
Kato’s strong Trotter product formula      379
Kernel      185 198
Lebesgue decomposition theorem      22—23 25
Lebesgue measure      15 13—18
Lebesgue — Stieltjes integral      19—2!
Leray — Schauder — Tychonoff theorem      151 365
liminf(dim)      11 12
limsup(lim)      11 12
Linear transformation      2
Linearly ordered      3
Locally compact      110
Locally convex spaces      125
Lower semicontinuous      355
Lusts of the flesh      249
Mackey topology      163
Mackey — Arens theorem      164 167—169
Mapping      1
Markov — Kakutani theorem      152
Maximum principle      382- 384
Measurable functions      15—16
Measure      23 104—111
Measure class      232
Measure, absolutely continuous      22 24
Measure, continuous      22
Measure, pure point      22
Measure, singular      22 24
Metric space      5
Metric transitivity      59
Minimization of functional      354- 363
Minkowski functional      128
Minkowski’s inequality      68 349
Mixing      239
Monotone convergence theorems for forms      372—377
Monotone convergence theorems for functions      17 24
Monotone convergence theorems for nets      106
Montel space      173
Multiplicity free operators      231
Multiplicity theory      231—234
Neighborhood      91
Neighborhood base      91
Nets      96 351
Neumann series      191
Norm      8
Norm resolvent sense, convergence in      284 284—291
Norm, equivalent      71
Normal operator      246
Normal space      94
Normed linear space      8
Nuciear theorem      141 144
One-parameter unitary group      265
Open function      92
Open mapping theorem      82 132
Open set      91
Operator      2
Operator, of uniform multiplicity      233
Orthocomplemented lattice      309—310
Orthogonal      37
Orthogonal complement      41
Orthonormal      37
Orthonormal basis      44 44—46
Paley — Wiener theorem      333
Parallelogram law      38 63
Parseval’s relation      45 46
Partial isometry      197
Partial ordering      3
Pettis’ theorem      119
Phragmen — Lindelof theorems      382—384 391
Plancherel theorem      327
polar      167
Polar decomposition      197 297—298
Polarization identity      63
Positive linear functional      106 350
Positive operator      195
Positive quadratic form      276
Positive type, distribution of      331
Positive type, function of      329
Positive type, weak      331
Principle of uniform boundedness      81 132
Product topology      94
Projection      187
Projection theorem      42
Projection, orthogonal      187
Projection-valued measure (p.v.m.)      234—235 262—263
Pythagorean Theorem      37
Quadratic form      276
quantum mechanics      302—305
Quotient space      78—79
Radon — Nikodym theorem      25 344
RANGE      2
Rectifiable      361
Reflexive space      74 167 174
Regular space      94
Regularity theorem for tempered distributions      139 144
Relative topology      95
Relatively open      95
Reproducing kernel      347
Resolvent      188 253
Resolvent set      188 253
Riemann — Lebesgue lemma      327
Riemann — Stieltjes integral      33
Riesz lemma      43 41—44
Riesz lemma, applications      344—348
Riesz — Markov theorem      107 111 353—354
Riesz — Schauder theorem      203
Schrodinger representation      274
Schwarz inequality      38
Second dual      74
Second quantization      302 309
Self-adjoint operator, bounded      187
Self-adjoint operator, unbounded      255
Self-adjointness, basic criterion for      256—257
Semibounded quadratic form      276
Seminorm      125
Separable      47 95
Separating hyperplane theorem      130—131
Sesquilinear form      44
Singular subspace      230
Singular value of a compact operator      203—204
Spectral mapping theorem      222
Spectral measures      228
Spectral measures, associated with a vector      225
Spectral projections      234
Spectral radius      192
Spectral radius, formula      192
Spectral representation      227
Spectral theorem, functional calculus form      225 263
Spectral theorem, multiplication operator form      225 263
Spectral theorem, p.v.m.form      235 263—264
Spectrum      188
Spectrum, absolutely continuous      231
Spectrum, continuous      231
Spectrum, continuous singular      231
Spectrum, discrete      236
Spectrum, essentia]      236

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