Birman M.S., Solomyak M.Z. — Spectral Theory of Self-Adjoint Operators in Hilbert Space :: Электронная библиотека попечительского совета мехмата МГУ

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Birman M.S., Solomyak M.Z. — Spectral Theory of Self-Adjoint Operators in Hilbert Space

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Название: Spectral Theory of Self-Adjoint Operators in Hilbert Space

Авторы: Birman M.S., Solomyak M.Z.

Язык:

Рубрика: Математика/Анализ/Функциональный анализ/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1987

Количество страниц: 301

Добавлена в каталог: 09.04.2005

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Предметный указатель

-system      280
-system      280
$[\rho]$ -absolutely continuous part of a spectral measure      180
$[\rho]$ -absolutely continuous part of a spectral measure, subspace for a spectral measure      180
$[\rho]$ -absolutely continuous part of a spectral measure, vector for a spectral measure      180
(B)-pair      287
(B)-pair, irreducible      290
(B)-system      281
(B)-system, irreducible      290
(C)-system      281
(C)-system, irreducible      294
Absolutely continuous measure r with respect to a measure $\mu$       11
Absolutely continuous measure r with respect to a measure $\mu$ of a self-adjoint operator      181
Absolutely continuous measure r with respect to a measure $\mu$ , part of a measure r with respect to a measure $\mu$       14
Absolutely continuous measure r with respect to a measure $\mu$ , subspace      181
Absolutely continuous measure r with respect to a measure $\mu$ , vector for a spectral measure      180
Additive function      4
Additive function, a-finite      4
Additive function, finite      4
Algebra of subsets      2
Algebra of subsets of subsets      3
Algebra of subsets, a-algebra of Borel subsets of a metric space      3
Algebraic multiplicity      78
Associate vector      77
Base of measurability      160
Base of measurability, orthogonal      160
Basis orthonormal      25
Basis orthonormal, standard in       26
Bose commutation relations      279
Calkin algebra      267
Canonical representation      243
Cayley transform      104
Class K      40
Class K,       13
Class K,       245
Class K,       250
Class K,       254
Class K, $S_{\infty}$       39
Class K,       15
Class K, $\dot{W}_2^l$       16
Class K, $\Phi$       259
Class K, $\sigma_p$       267
Closure of a linear operator      66
Commutation relations of quantum mechanics      279
Commutation relations of quantum mechanics, canonical      279
Commuting bounded operators      37
Commuting operators      61
Complete subset of a Hilbert space      20
Continuous singular spectrum      182
Continuous singular spectrum, subspace      182
Core of the spectrum      83
Defect number of a closed operator      82
Defect of a closed operator      81
Defect of a closed operator of a linear set      63
Deficiency indices of a symmetric operator of an isometric operator      101
Derivative of a measure r with respect to a measure ju      11
Dimension function      158
Direct integral of Hilbert spaces      162
Direct sum of linear subsets      63
Distribution function      114
Distribution function of eigen-values      273
Distribution function of s-numbers      245
Domain of an operator      60
Domination of operators      73
Domination of operators, strong      74
Eigen-space      77
Eigen-value of an operator      77
Equivalent measures      11
Extension of an operator      61
Family of projections closed under multiplication      47
Form of an operator      35
Form, closed      221
Form, lower semibounded      221
Form, positive definite      221
Form, quadratic      35
Form, sesqui-linear      35
Fourier coefficients      23
Fourier coefficients, series      23
Fourier coefficients, transform      192
Fredholm alternative      89
Friedrichs extension      229
Function of a self-adjoint operator      142
Function, a-finite      4
Function, additive      4
Function, countably additive      4
Function, finite      4
Functional, antilinear      32
Functional, continuous linear      32
Functional, Hermitian      34
Functional, quadratic      34
Functional, sesqui-linear      33
Generalized derivative      15
Generating system      170
Generating vector      175
Generator of a unitary group      151
Geometric multiplicity      78
Graph of an operator      62
Greatest lower bounded of a bounded operator      42
Greatest lower bounded of a bounded operator of a quadratic form      221
Hardy inequality      55
Hardy operator      55
hatch of a symmetric operator      216
Heinz inequality      232
Hermite polynomials      48
Hilbert identity      84
Hilbert space      19
Hilbert — Schmidt kernel      252
Hilbert — Schmidt kernel, operator      250
Hilbert — Schmidt kernel, operator-valued kernel      253
Horn’s inequalities      262
Inner product in a pre-Hilbert space      18
Integral with respect to a spectral measure      132
Involution      1
Isometric isomorphism of Hilbert space      19
Jordan chain      77
Kernel of a linear operator      60
Kernel of an integral operator      52
Kernel of an integral operator, Hermitian      52
Least upper bound of a bounded operator      42
Lidskii’s theorem      268
Linear sum of linear subsets      63
Measurable function      7
Measurable Hilbert family      161
Measurable set      3
Measure      4
Measure space      4
Measure space, separable      5
Measure with countable base      5
Measure, Borel      6
Measure, Borel spectral      128
Measure, complex      12
Measure, N-complete      4
Measure, simple spectral      175

Measure, spectral      123
Modulus of a closed operator      184
Multiplication by the independent variable      112
Multiplication operator      163
Multiplicity function      172
Multiplicity of a spectral measure      178
Multiplicity of the spectrum      177
Mutually singular measures      13
Mutually singular measures, types      13
Natural boundary condition      234
Norm in a pre-Hilbert space      18
Norm in a pre-Hilbert space, a-norm      221
Normal eigen-value      83
One-parameter unitary group      150
Operator of finite rank      40
Operator polynomials      67
Operator, adjoint      69
Operator, adjoint to a bounded operator      35
Operator, bounded, non-negative      42
Operator, bounded, normal      44
Operator, bounded, positive      43
Operator, bounded, positive definite      43
Operator, bounded, self-adjoint      41
Operator, bounded, strictly positive      43
Operator, closable      66
Operator, closed      64
Operator, commuting with a self-adjoint operator      150
Operator, compact      39
Operator, decomposable      168
Operator, differential with constant coefficients      197
Operator, essentially self-adjoint      98
Operator, integral      52
Operator, isometric      100
Operator, lower semibounded      99
Operator, maximal symmetric      97
Operator, normal      109
Operator, nuclear      245
Operator, partially isometric      102
Operator, positive      99
Operator, positive definite      99
Operator, regular integral      52
Operator, self-adjoint      97
Operator, self-adjoint with simple spectrum      177
Operator, semiunitary      103
Operator, symmetric      97
Operator, unitary      101
Order of a root lineal      78
Orthogonal complement      27
Orthogonal sum of Hilbert spaces      29
Orthogonal sum of subspaces      28
Orthogonalization process      25
Orthonormal system      23
Orthonormal system, closed      24
Orthonormal system, complete      24
Polar decomposition      183
Pre-Hilbert space      18
Principle maximin      212
Principle minimax      212
Product of measures      6
Product of spectral measures      129
Projection      27
Quasi-regular point      82
Quasi-regular set      82
Range of an operator      60
Regular point      83
Resolution of the identity      140
Resolvent      84
Resolvent set of an operator      83
Riesz projection      269
Root lineal of an operator      77
Root space of an operator      77
Rotfel’d’s theorem      261
Schmidt expansion      243
Simple function      8
Sine of the angle between subspaces      88
Singular numbers of a compact operator      182
Singular part of a measure r with respect to a measure $\mu$       14
Singular part of a self-adjoint operator      181
Singular sequence for a self-adjoint operator      206
Skew decomposition      86
Skew decomposition, projection      86
Skew decomposition, reducing decomposition      88
Space, $B(H_1, H_2)      39
Space, $L_2(Y, \mu, b)$       30
Space,       22
Space,       30
Space, $L_p(Y, \mu)$       10
Space, $L_{\infty}(Y, E)$       130
Space, $L_{\infty}(Y, \mu)$       8
Space, B(H)      36
Space, S(Y, E)      133
Spectral mapping property      158
Spectral measure space      123
Spectral resolution      140
Spectral trace      268
Spectrally orthogonal subspaces      170
Spectrally orthogonal subspaces, vectors      170
Spectrum      83
Spectrum, continuous      83
Spectrum, discrete      206
Spectrum, essential      206
Spectrum, joint of a system of operators      154
Spectrum, point      83
Spectrum, purely continuous      112
Spectrum, purely point      112
Spectrum, residual      83
Strong convergence of operators      36
Strongly commuting operators      61
Subspace of a Hilbert space      20
Subspace of a Hilbert space, invariant      76
Subspace of a Hilbert space, reducing      79
Support of a Borel measure      7
Support of a Borel measure, spectral measure      129
Support of a measure $\tau$ with respect to a measure $\mu$       11
Support of a type $[\tau]$ with respect to a type $[\mu]$       11
Topologically consistent norms      2
Trace of an operator      248
Type of a measure      11
Type of a vector with respect to a spectral measure      170
Type, maximal      171
Type, spectral      171
Uniform convergence of an operator      36
Unitary equivalent operators      103
Unitary equivalent operators, invariant      103
Vector of maximal type      171
von Neumann’s formulae      106
Weak convergence of operators      36
Weak convergence of vectors      33
Weyl’s criterion      207
Weyl’s inequalities      213
[\rho]-singular part of a spectral measure      180
[\rho]-singular subspace for a spectral measure      180
[\rho]-singular vector for a spectral measure      180

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