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Reed M., Simon B. — Methods of Modern mathematical physics (vol. 4) Analysis of operators
Reed M., Simon B. — Methods of Modern mathematical physics (vol. 4) Analysis of operators



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Название: Methods of Modern mathematical physics (vol. 4) Analysis of operators

Авторы: Reed M., Simon B.

Аннотация:

The book covers the theory about eigenvalues of Schrodinger operators. It is complete success in explaining clearly the basic concepts involved: perturbation theory (summability questions, fermi golden rule), min-max principle for discrete spectrum, Weyl theorem, HVZ theorem, the absence of singular continuous spectrum, ground state questions, periodic operators, semiclassic distribution of eigenvalues, compactness criteria.


Язык: en

Рубрика: Математика/Математическая Физика/Учебники/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1978

Количество страниц: 396

Добавлена в каталог: 24.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Operator, non-self-adjoint      316—338
Operator, norm      $9^1$
Operator, normal      $246^1$
Operator, positive      195
Operator, positivity improving      201
Operator, positivity preserving      201
Operator, relatively bounded      $162^2$
Operator, relatively compact      113
Operator, relatively form bounded      $168^2$
Operator, relatively form compact      369
Operator, resolvent      $188^1$
Operator, Schrodinger      79
Operator, self-adjoint      $187^1$
Operator, smooth      142
Operator, symmetric      $255^1$
Operator, tensor product      $299^1$
Operator, topologies      $182^1$—$185^1$
Operator, trace class      $207^1$—$210^1$
Operator, unbounded, general theory      $249^1$—$312^1$
Order k strong asymptotic series      43
O’Connor — Combes — Thomas theorem      198
O’Connor’s lemma      196
Paley — Wiener theorems      $16^2$
Parseval’s relation      $45^1$—$46^1$
Part of the spectrum in X      46
Partial trace      382
Period cell      303
Periodic potentials      279
Perron — Frobenius theorems      202 350
Perturbation series      2
Perturbation series, asymptotic      26
Perturbation series, Puiseux      4
Perturbation series, Raleigh — Schrodinger      1
Perturbation series, strong asymptotic      40
Perturbation series, wildly divergent      27
Phase space      $313^2$
Phragmen — Lindelof principle      236
Plancherel theorem      $10^2$
Plemelj — Smithies formulas      332
Poisson bracket      $314^2$
Poisson summation formula      380
Polar decomposition      $197^1$
Polarization identity      $63^1$
Positive definite      see also “Positive type”
Positive definite, conditionally      214
Positive distribution      $182^2$
Positive function      201
Positive operator      $195^1$
Positive type, distribution      $14^2$
Positive type, function      $12^2$
Positivity improving operator      201
Positivity preserving operator      $186^2$ 201
Principle of uniform boundedness      $81^1$
Product formula      $295^1$—$297^1$
Projection      $187^1$
Projection valued measure (p.v.m.)      $234^1$—$235^1$
Pseudo-eigenvalue      48
Pseudo-eigenvector      48
Puiseux series      4
Putnam — Kato theorem      157
Quadratic forms      $276^1$
Quadratic forms, closed      $277^1$
Quadratic forms, form core      $277^1$
Quadratic forms, form domain      $276^1$
Quadratic forms, Friedrichs’ extension      $177^2$
Quadratic forms, infinitesimally bounded      $168^2$
Quadratic forms, positive      $276^1$
Quadratic forms, relatively bounded      $168^2$
Quadratic forms, relatively compact      369
Quadratic forms, Riesz lemma      $43^1$
Quadratic forms, semi-bounded      $276^1$
Quadratic forms, strictly m-accretive      $281^1$
Quadratic forms, strictly m-sectorial      $282^1$
Quadratic forms, symmetric      $276^1$
Radius of gyration      197
Radon — Nikodym theorem      $25^1$
Rayleigh — Ritz technique      82
Rayleigh — Schrddinger coefficients      5—8
Rayleigh — Schrddinger series      1 5
Rayleigh’s theorem      364
Reduced disconnected part      131
Reduced resolvent      130
Relatively bounded      $162^2$
Relatively compact      113
Relatively form bounded      $168^2$
Relatively form compact      369
Rellich’s criterion      247
Rellich’s theorem      4
Resolvent      $188^1$
Resolvent set      $188^1$
Resonance eigenvalues      191
Resonance pole      55
Resonance thresholds      191
Retardation term      81
Riccati equation      96
Riemann — Lebesgue lemma      $10^2$
Riesz’s criterion      248
Riesz’s lemma      $43^1$
Rollnik potential      $170^2$
Scale of spaces      $278^1$
Schrodinger equation      $303^1$
Schrodinger operators      79
Schur basis      318
Schur — Lalesco — Weyl theorem      318
Schwartz space      $133^1$
Schwarz inequality      $38^1$
Secular equation      2
Segment property      256
Self-adjoint operator, bounded      $187^1$
Self-adjoint operator, unbounded      $255^1$
Semibounded operator      $137^2$
Semibounded quadratic form      $276^1$
Semigroup, $L^p$-contractive      $255^2$
Semigroup, contraction      $235^2$
Semigroup, holomorphic      $248^2$
Semigroup, hypercontractive      $258^2$
Semigroup, infinitesimal generator      $237^2$
Semigroup, strongly continuous      $235^2$
Singular support      $88^2$
Singular value of a compact operator      $203^1$
Smooth operator      142
Sobolev inequality      $31^2$
Sobolev lemma      $52^2$
Sobolev spaces      $50^2$ 253
Solid state theory      311
Sommerfeld correction      80
Spectral concentration      45—50
Spectral mapping theorem      $222^1$ 109 181—183
Spectral measures      $228^1$
Spectral measures, associated with a vector      $225^1$
Spectral projections      $234^1$
Spectral theorem, functional calculus form      $225^1$
Spectral theorem, multiplication operator form      $227^1$
Spectral theorem, p.v.m. form      $235^1$
Spectrum      118
Spectrum,absolutely continuous      $231^1$
Spectrum,approximate point      178
Spectrum,asymptotically in a set      46
Spectrum,continuous      $231^1$
Spectrum,continuous singular      $231^1$
Spectrum,discrete      $236^1$ 13
Spectrum,essential      $236^1$
Spectrum,point      $188^1$
Spectrum,residual      $188^1$
Spin-orbit correction      80
Spin-spin interaction      81
Stable eigenvalue      29
Standard $2^{-n}$ cube      271
Stark effect      $200^2$ 50 118
Stone’s formula      $237^1$
Stone’s theorem      $265^1$—$267^1$
Strichartz’s theorem      $171^2$ 378
Strictly m-accretive form      $281^1$
Strictly m-accretive operator      $281^1$
Strictly m-sectorial form      $282^1$
Strictly positive function      201
String      129
Strong asymptotic series      40
Strong operator topology      $182^1$
Strong resolvent sense, convergence in      $284^1$—$291^1$
Strongly continuous semigroup      235
Strongly continuous unitary group      265
Strongly measurable      $64^1$
Sturm oscillation theorem      92
Summability methods, Borel      44
Summability methods, Pade      63
Summability methods, regular      63
Support of a distribution      $139^1$
Support of a distribution, singular      $88^2$
Symmetric operator      $255^1$
Symmetric quadratic form      $276^1$
Tempered distributions      $134^1$
Temple’s inequality      84
Temple’s inequality, generalized      365
Tensor product, Hilbert spaces      $49^1$
Tensor product, operators      $299^1$
Tensor product, spectrum of      177
Time-dependent perturbation theory      51—60 66—68
Total mass      197
Trace class      207—$210^1$
Trotter product formula      $295^1$—$297^1$
Trotter — Kato theorem      $288^1$
Uncertainty principle lemma      $169^2$
Uniform boundedness principle      see “Principle of uniform boundedness”
Uniform operator topology      $182^1$
Uniformly Holder continuous      191
Uniformly locally $L^p$      302
Unique continuation      226 239
Unitary operator      $39^1$
Virial theorem      231
von Neumann’s theorem      $268^1$
von Neumann’s uniqueness theorem      $275^1$
Watson’s theorem      44
Weak derivative      $138^1$
Weak graph limit      $294^1$
Weak topology      $93^1$
Weak-$L^p$      $30^2$
Weak-$L^p$, inequalities      $32^2$
Weakly measurable (vector-valued) function      $114^1$
Weighted $L_2$ space      $76^2$ 168
Weinberg kernel      125
Weinberg kernel, symmetrized      131
Weinberg — Van Winter equation      126
Weyl relations      $275^1$
Weyl’s criterion      $237^1$
Weyl’s lemma      $53^2$
Weyl’s theorem, classical      117
Weyl’s theorem, essential spectrum      112
Width of a resonance      55
Wiener measure      $278^2$
Wiener measure, conditional      102
Wigner — Seitz cell      311
Wigner — von Neumann potential      223
wronskian      $150^2$
Young’s inequality      282
Zhislin’s theorem      89
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