Главная    Ex Libris    Книги    Журналы    Статьи    Серии    Каталог    Wanted    Загрузка    ХудЛит    Справка    Поиск по индексам    Поиск    Форум   
blank
Авторизация

       
blank
Поиск по указателям

blank
blank
blank
Красота
blank
Akhiezer N.I., Glazman I.M. — Theory of Linear Operators in Hilbert Space
Akhiezer N.I., Glazman I.M. — Theory of Linear Operators in Hilbert Space



Обсудите книгу на научном форуме



Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter


Название: Theory of Linear Operators in Hilbert Space

Авторы: Akhiezer N.I., Glazman I.M.

Аннотация:

This classic textbook introduces linear operators in Hilbert Space, and presents the geometry of Hilbert space and the spectral theory of unitary and self-adjoint operators. 1961, 1963 edition.

This classic textbook by two mathematicians from the U.S.S.R.'s prestigious Kharkov Mathematics Institute introduces linear operators in Hilbert space, and presents in detail the geometry of Hilbert space and the spectral theory of unitary and self-adjoint operators. It is directed to students at graduate and advanced undergraduate levels, but because of the exceptional clarity of its theoretical presentation and the inclusion of results obtained by Soviet mathematicians, it should prove invaluable for every mathematician and physicist. 1961, 1963 edition.


Язык: en

Рубрика: Математика/Анализ/Функциональный анализ/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1993

Количество страниц: 218

Добавлена в каталог: 09.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
blank
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
blank
Реклама
blank
blank
HR
@Mail.ru
       © Электронная библиотека попечительского совета мехмата МГУ, 2004-2020
Электронная библиотека мехмата МГУ | Valid HTML 4.01! | Valid CSS! О проекте