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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
$C^{\infty}$-vector      $201^2$
$L^p$ inequalities      32
Absolute value of an operator      $196^1$
Absolutely continuous subspace      $230^1$
Accretive operator      $240^2$
Adjoint, Banach space      $185^1$
Adjoint, Hilbert space      $186^1$
Adjoint, unbounded operator      $252^1$
Agmon potential      169
Agmon — Kato — Kuroda theorem      169
Algebraic multiplicity      9
Analytic family of type (b)      20
Analytic family, in the sense of Kato      14
Analytic family, type (A)      16
Analytic family, type (B)      20
Analytic Fredholm theorem      $201^1$
Analytic function, vector-valued      $189—190^1$
Analytic vector      $201^2$
Anharmonic oscillator      $175^2$ 20 32 41 64 84
Antilinear operator      $69^1$
Approximate identity      $251^1$
Approximate point spectrum      178
Aronszajn — Donoghue theory      140
Ascoli’s Theorem      $30^1$
Associated string      129
Asymptotic series      26
Asymptotic series, order k strong      43
Asymptotic series, strong      40
Atomic model      304
Auger states      52
Autoionizing states      52
Axiomatic quantum field theory      $62^2$
B.L.T. theorem      $9^1$
Baire measure      $105^1$
Balslev — Simon theorem      237
Banach space      $67^1$
Barely connected      125
Bargmann’s bound      94 366
Basic period cell      303
Basis of a lattice      310
Bessel’s inequality      $38^1$
Beurling — Deny criteria      209
Birman — Schwinger bound      98
Bochner integral      $119^1$
Bochner — Schwartz theorem      $14^2$
Borel set      $14^1$
Borel summability method      44
Borel transform      44
Borel — Caratheodory theorem      328
Boson Fock space      $53^1$
Bound state energies      79
Bound states      79
Bounded holomorphic semigroup      $248^2$
Bounded operator      $8^1$
Breit — Wigner resonance shape      53
Brillouin zone      311
Calogero’s bound      94 366
Canonical commutation relations      $274^1$
Canonical form for compact operators      $203^1$
Carleman’s theorem      39
Carlson’s theorem      236
Cauchy sequence      $5^1$
Center of mass      197
Central potential      90
Characteristic equation      2
Characteristic function      $2^1$ 221
Classical Weyl theorem      117
Closed graph theorem      $83^1$
Closed operator      $250^1$l
Closed quadratic form      $277^1$
Cluster decomposition      129
Commuting (unbounded) operators      $271^1$—$272^1$
Compact operator      $199^1$ (see also “Relatively compact” “Relatively
Compact operator, determinant      323 382
Compact operator, general theory      $198^1$—$206^1$ 316—338
Compact operator, Hilbert — Schmidt      $210^1$
Compact operator, ideal theory      $41^2$—$44^2$
Compact operator, resolvent      244—260
Compact operator, trace class      $206^1$—$213^1$
Compact sets      $97^1$ 244
Compact support, distributions      $139^1$
Compact support, functions      $111^1$
Complex scaling      see “Dilation analytic potentials”
Complex thresholds      191
Conditionally negative definite      215
Conditionally positive definite      214
Contented set      271
Continuous functional calculus      $222^1$
Contraction semigroup      $235^2$
Convex function      104
Convex set      $109^1$
Convolution, distributions      $7^2$
Convolution, functions      $6^2$
Core      $256^1$
Coupling constant      11
Critical value      346
Cwikel — Lieb — Rosenbljum bound      101
D-thresholds      189
Darwin correction      81
Decomposable operator      281
Deficiency indices      $138^2$
Degenerate eigenvalue      2
Density of states      313
Density of states measure      312
Determinant      323 382
Diagram, barely connected      125
Diagram, disconnected      125
Diagram, k-connected      129
Dilation analytic potentials      184
Dilation operators      56 183
Dirac operator      $337^2$
Direct integral      280 358
Direct sum, of Banach spaces      $78^1$
Direct sum, of Hilbert spaces      $40^1$
Dirichlet Laplacian      263
Dirichlet problem      $204^1$
Dirichlet — Neumann bracketing      262
Disconnected part      125
Disconnected string      129
Discrete spectrum      $236^1$ 13
Discriminant      296
Distribution of eigenvalues, Dirichlet Laplacian      260
Distribution of eigenvalues, Schrodinger operators      86
Distributions, compact support      $139^1$
Distributions, tempered      $134^1$
Domain, analytic function      $189^1$
Domain, form      $276^1$
Domain, function      $2^1$
Domain, unbounded operator      $249^1$
Dominated Convergence Theorem      $17^1$
Double well potential      34
Dual basis      305
Dual space      $43^1$
Dunford functional calculus      $245^1$
Dyson expansion      $282^2$
Eigenvalue      $188^1$
Eigenvalue, degenerate      2
Eigenvalue, discrete      13
Eigenvalue, multiplicity      9 316
Eigenvalue, nondegenerate      9 13
Eigenvalue, pseudo      48
Eigenvalue, simple      9
Eigenvalue, stable      29
Eigenvector      $188^1$
Eigenvector, generalized      316
Eigenvector, pseudo-      48
Elliptic operator      $112^2$ 346
Elliptic regularity      $49^2$
energy levels      11 79
Energy operator      see “Hamiltonian”
Equicontinuous function      $28^1$—$30^1$
Ergodic operator      202
Essentially self-adjoint      $256^1$
Exceptional set      § XI.6 Vol.
Extension of an operator      $250^1$
Fan’s inequality      383
Fermi energy      314
Fermi gas picture      356
Fermi Golden Rule      52 59
Fermi statistics      $117^2$
Fermi surface      314
Fermion Fock space      $54^1$
Feynman — Kac formula      $279^2$
Fibers      280—281
Finite partition      208
First resolvent formula      1911
Fock space      53!
FORM      see also “Quadratic forms”
Form, core      $277^1$
Form, domain      $276^1$
Form, domain, of operator      $277^1$
Formal series      73
Fourier inversion theorem      $3^2$
Fourier transform      $1^2$
Friedrichs’ extension      $177^2$
Functional calculus      $222^1$ 245
Functions of rapid decrease      $133^1$
Generalized eigenspace      9
Generalized eigenvector      316
Generalized function      $148^1$
Generator group      268l
Generator semigroup      $237^2$
Geometric eigenspace      9
Geometric multiplicity      9
GGMT bound      94
Ghirardi — Rimini bound      367
Golden — Thompson inequality      $333^2$
Graph      831 250
Graph limits      293
Green’s functions      592 263
Ground state      201
Ground state energy      201
Gyration, radius of      197
H-smooth on $\Omega$      163
H-smooth operator      142
Hadamard’s three line theorem      $33^2$
Hahn — Banach theorem      $75^1$—$77^1$
Hamiltonian      $303^1$
Hamiltonian, free      $55^2$
Hamiltonian, time dependent      $109^2$
Hausdorff — Young inequality      $11^2$
Helium Hamiltonian      80
Hermite functions      $142^1$
Hermite functions, completeness      $121^2$
Hermitian operator      see “Symmetric operator”
Hilbert space      $36^1$
Hilbert — Schmidt operators      $210^1$
Hilbert — Schmidt theorem      $203^1$
Holder continuous      $81^2$ 191
Holder’s Inequality      $68^1$
Holder’s inequality, matrices      385
Holder’s inequality, operators      $41^2$
Holomorphic semigroup      $252^2$
Holomorphic semigroup, bounded      $248^2$
Hughes-Eckart term      80
Hunziker’s theorem      see “HVZ theorem”
HVZ theorem      121
Hypercontractive semigroup      $258^2$
Hyperfine structure in hydrogen      19
Ichinose’s lemma      183
Index of a string      129
Infinitely divisible      221
Infinitesimal generator, group      $268^1$
Infinitesimal generator, semigroup      $237^2$
Infinitesimally small form      $168^2$
Infinitesimally small operator      $162^2$
Interpolation theorems      $32^2$
Inverse Fourier transform      $1^2$
Iorio — O’Carroll theorem      154
Irreducible      $232^2$
Jensen’s inequality (17)      104
Jordan content      271
Jordan normal form      10
Jost solution      §XI.8 Vol.
k-connected diagram      129
Kato — Agmon — Simon theorem      226
Kato — Rellich theorems      $162^2$ 15
Kato — Simon theorem      193
Kato’s inequality      $183^2$ 351
Kato’s projection theorem      22
Kato’s smoothness theorem      152
Kato’s theorem      $166^2$
KLMN theorem      $167^2$
Kohn’s theorem      301
Korteweg-de Vries equation      300
Kronig — Penny model      381
Lamb shift      81 86
Laplacian, Dirichlet      263
Laplacian, Neumann      263
Laplacian, on $\mathbb{R}^n$      $54^2$
Lattice, ordered sense      $310^1$
Lattice, subgroup sense      310
Lavine’s theorem      159
Levy — Khintchine formula      215
Levy — Khintchine Theorem      221
Lidskii’s theorem      328
Lieb — Thirring bound      368
Lipschitz      154
Local smoothness (operators)      163
Local Sobolev spaces      $51^2$ 253
m-accretive      $168^1$
Mathieu equation      $320^2$ 298
Measurable functions, sets      $14^1$—$16^1$
Measurable unbounded operator-valued function      283
Measurable, weakly and strongly      64
Measure      $19^1$—$25^1$
Meromorphic Fredholm theorem      107
Min-max principle      76
Monotone Convergence Theorem      $17^1$
Monotone convergence theorem, for nets      $106^1$
Multiplicity of an eigenvalue      9
Multiplicity theorem      $231^1$
Neumann Laplacian      263
Norm      $8^1$
Norm resolvent sense, convergence in      $284^1$—$291^1$
Norm, operator      $9^1$
Normal coordinates      197
Normal operator      $246^1$
One-electron model of solids      312
One-parameter unitary group      $265^1$
Operator, adjoint, Banach space      $185^1$
Operator, adjoint, Hilbert space      $186^1$
Operator, adjoint, unbounded      $252^1$
Operator, bounded      $8^1$
Operator, compact      $199^1$
Operator, compact resolvent      244
Operator, contraction      $151^1$
Operator, decomposable      281
Operator, dilation      183
Operator, elliptic      $112^2$ 346
Operator, energy (Hamiltonian)      $303^1$
Operator, general theory      $81^1$—$84^1$
Operator, Hamiltonian      $303^1$
Operator, Hermetian      see “Operator symmetric”
Operator, Hilbert — Schmidt      $210^1$
Operator, ideals      $41^1$—$44^2$
Operator, infinitesimally form small      $168^2$
Operator, infinitesimally small      $162^2$
Operator, locally smooth      163
Operator, momentum      $304^1$
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