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| Авторизация |
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| Akhiezer N.I., Glazman I.M. — Theory of Linear Operators in Hilbert Space |
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| Предметный указатель |
Additive interval function 56
Basis, generating 63
Bessel functions 211
Canonical form of an operator 52 64
Carleman kernel 184
Cayley transform 42 94
Cayley transform of a symmetric operator 43
Characteristic function of an operator 152 153
Commutative operator 76
Deficiency 93
Deficiency, element 93
Deficiency, indices 91
Deficiency, number 93
Deficiency, subspace 93
Differential expressions 162
Differential operator 84 106 203
Dimension modulo M 98
Direction functional 187
Discrete part of the spectral kernel 107
Distribution function 56 61
Distribution function, inferior 56
Eigen-frequency of a unitary operator 48
Eigenvalue 46
Elementary maximal operators 106
Equivalent, unitarily 65
Extensions 96
Extensions, quasi-self-adjoint 146
Extensions, quasi-unitary 148
Extensions, reduced conditions 198
Extensions, relatively prime 1 !0
Extensions, self-adjoint 107 108 110 167 174
Extensions, symmetric 100 108 110 127
Field of regularity 91
Fourier — Bessel series 214
Fourier — Dienes series 214
Fourier — Plancherel transforms 186 206
Functionals, direction 187
Functions of self-adjoint operators 68
Functions, additive interval 56
Functions, Bessel 211
Functions, characteristic vector 61
Functions, distribution 56 61
Functions, Legendre 206
Functions, Tchebysheff — Hermite 210
Functions, trigonometric 204
Generalized resolvent 134
Generating basis 63
Generating subspace 59
Groups of unitary operators 29
Hankel transform 213
Hilbert — Schmidt kernel 184
Identity, resolution of 14 16
Identity, resolution of, linear 97
Identity, resolution of, modulo M 98
Inferior distribution functions 56
Integral operator with Carleman kernel 184
Integral operator with Hilbert — Schmidt kernel 183
Integral representation of a group of unitary operators 29
Integral representation of a resolvent 31
Integral representation of a unitary operator 16
Integral representation of analytic functions 5 7 8
Integral representation of self-adjoint operators 36
Inversion formulas 186
Inversion formulas of self-adjoint operators 186
Inversion formulas, Weber 215
Kernel, Carleman 184
Kernel, Hilbert — Schmidt 183
Kernel, spectral 107
Krein formula 110 139
Lagrange identity 163
Legendre functions 206
Limit, circle 176 199
Limit, point 176 199
Linear independence 97
Linear independence, modulo M 98
Maximal common part 110
Maximal operators 103 106
Moment problem 1
Neumann formulas 97 99
Operators, canonical form of 64
| Operators, characteristic functions of 152 153
Operators, commutative 76
Operators, differential 84 106 203
Operators, multiplication 50 62 84
Operators, rings of 80
Operators, semi-bounded 114
Operators, simple symmetric 101
Orthogonal resolution of the identity 16 121
Orthogonal resolvent 134
Point of constancy 46
Point of continuous growth 46
Point of growth 46
Point of regular type 91
Point, continuity 46
Point, jump 46
Point, regular 46
Quasi-differential operation 162 186
Quasi-differential operation, regular 163
Quasi-differential operation, singular 163
Quasi-regular differential operator 176
Quasi-scalar product 123
Quasi-self-adjoint extensions 146
Quasi-unitary extension 148
Regular differential operators 166
Regular point 46
Regular quasi-differential expression 163
Regular quasi-differential operator 168
Resolution of the identity 14 16 121
Resolution of the identity, generalized 121
Resolvents 110
Resolvents of self-adjoint extensions 177
Resolvents, generalized 134
Resolvents, integral representation 29 31
Resolvents, orthogonal 134
Rings of operators 80
Self-adjoint extensions 107 108 110 167 174
Self-adjoint operators, canonical form 52 60
Self-adjoint operators, differential expressions 162
Self-adjoint operators, functions of 68
Self-adjoint operators, integral representation of 36
Self-adjoint operators, rings of bounded 80
Self-adjoint operators, spectra of 46
Self-adjoint operators, unitary invariants of 65
Semi-bounded operators 114
Series, Fourier — Bessel 214
Series, Fourier — Dienes 214
Simple spectrum 50
Simple symmetric operators 101
Singular differential operators 170
Singular quasi-differential expression 163
Spectral function 49 134
Spectral kernel 107
Spectral types 56
Spectrum 46
Spectrum, multiple 59
Spectrum, multiplicity of 59
Spectrum, simple 50
Stieltjes integrals 22
Subspace, deficiency 93
Subspace, generating 93
Tchebysheff — Hermite functions 210
Theorem of Bochner 11
Theorem of J. von Neumann 104
Theorem of M. A. Naimark 124
Theorem of R. Nevanlinna 7
Theorem of Riesz — Neumann 77
Transform, Cayley 42 94
Transform, Fourier — Plancherel 186 206
Transform, Hankel 213
Trigonometric functions 204
Unitarily equivalent 65
Unitary invariants 65
Unitary operators 16 29
Unitary operators, eigen-frequency of 48
Unitary operators, groups of 29
Unitary operators, spectra of 46
Weakly closed operator ring 81
Weber inversion formulas 215
Weyl limit, circle 176 199
Weyl limit, point 176 199
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