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Gorbachuk M., Gorbachuk V. — M. G. Krein's Lectures on Entire Operators
Gorbachuk M., Gorbachuk V. — M. G. Krein's Lectures on Entire Operators

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Название: M. G. Krein's Lectures on Entire Operators

Авторы: Gorbachuk M., Gorbachuk V.


This book is devoted to the theory of entire operators, founded by one of the century's best known mathematicians, M.G. Krein. The theory lies at the junction of the spectral theory of Hermitian operators and the theory of analytic functions, harmoniously combining the methods of each. The purpose of the book is to show how various problems of classical and modern analysis can be looked at from the entire operator theory point of view. This is the first systematic presentation of basic concepts of Krein's theory and its applications. The present study of Krein's unpublished lectures and his works gives (over)due recognition to the unique approach he developed - an approach which for many years was not broadly known. The book is intended for researchers as well as graduate and postgraduate students interested in the spectral theory of operators, complex analysis, differential equations and extrapolation problems.

Язык: en

Рубрика: Математика/Анализ/Функциональный анализ/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1997

Количество страниц: 220

Добавлена в каталог: 09.04.2005

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Предметный указатель
Arc, spiral      141
Arc, unitary      141
Caley transform      8
Canonical solution of the continuation problem for positive definite functions      139
Canonical solution of the power moment problem      125
Chain of entire projectors      206
Class, $\mathfrak{B}_{2T}$      157
Class, $\mathfrak{S}(\mathfrak{h}_1, \mathfrak{h}_2)$      162
Class, $\mathfrak{S}^k$      162
Closure of an operator      2
Complete continuation of a spiral arc      141
Complete continuation of a spiral arc, canonical      153
Continuation problem for positive, definite functions, definite      131
Continuation problem for positive, definite functions, indefinite      131
Convex domain      39
Defect number      4
Deficiency index      4
Dimension modulo      4
Directing functional      99
Directing functional, universal      109
Eigenvalue      2
Eigenvector      2
Entire projector      206
Extended spectral function      174
Extension of an operator      1
Extension with exit      4
Extension within      4
Function of completely regular growth      44
Function of the first kind      165
Function of the second kind      165
Function of weak bounded variation      161
Function, $R_0$-function      73
Function, $\nabla_M(z)$      60
Function, Blaschke      28
Function, canonical distribution      51
Function, correlation of a unitary arc      142
Function, distribution      48
Function, distribution associated with a gauge      49
Function, e(z)      59
Function, metric of a spiral arc      141
Function, N-function      24
Function, positive definite      126
Function, R-function      70
Function, regular      14
Function, subharmonic      21
Function, support      39
Gauge      11
Gauge, entire      61
Gauge, generalized quasilinear      117
Gauge, quasiregular      49
Generalization of a directing functional      193
Generalization of the Stieltjes inversion formula (rule)      12
Generalized element      110
Generalized maximum principle      23
Graph of an operator      2
Hilbert scale      178
Indicator      42
Indicator diagram      43
Indicator, trigonometric      42
Involution      90
Jensen formula      22
Line, spiral      141
Line, unitary      141
Linearly independent sets      3
Module of a representation      11
Multiplicity of an eigenvalue      2
Nevanlinna criterion      27
Nevanlinna matrix      93
Operator, adjoint      3
Operator, closable      2
Operator, closed      1
Operator, entire      62
Operator, entire of minimal type      66
Operator, entire of normal type      66
Operator, hermitian      3
Operator, J-real      92
Operator, M-entire      169
Operator, maximal      178
Operator, maximal Hermitian      8
Operator, minimal      177 178
Operator, real with respect to an involution      90 91
Operator, regular      20
Operator, self-ajoint      3
Operator, simple      10
Point of regular type      17
Point of support      40
Point, M-regular      164
Point, regular of a function      14
Point, regular of an operator      2
Point, u-regular      56
Power moment problem      120
Power moment problem, definite      122
Power moment problem, indefinite      122
Resolution of the identity      4
Resolution of the identity, orthogonal      5
Resolvent      2
Resolvent identity ( Hilbert)      2
Resolvent, extended generalized      173
Resolvent, generalized      74
Resolvent, orthogonal (canonical)      74
Set, $C_0^1(\mathbb{R}^1)$      100
Set, $V_u$      49
Set, $V_{\tilde{u}}$      117
Set, $\mathfrak{R}$      49
Set, C(M)      171
Set, S(A, M)      111
Solution of the equation      178
Solution of the equation, weak      178
Space with negative norm      111
Space with positive norm      111
Space, $\mathfrak{h}_+$      111
Space, $\mathfrak{h}_-$      111
Space, $\mathfrak{h}_{\mathfrak{L}}$      102
Space, L2(R\d<7)      48
Spectral function of a Hermitian operator      7
Spectral function of a self-adjoint operator      6
Spectral lacuna      17
Spectrum      2
Spectrum, continuous      2
Spectrum, discrete      20
Spectrum, point      2
Spectrum, residual      3
Spectrum, simple      200
Stieltjes inversion formula (rule)      12
Supporting straight line      39
Theorem, Naimark      7
Theorem, Phragmen — Lindelof for subharmonic functions      23
Theorem, principal spectral      6
Vector, compactly supported      207
Vector, generating      200 201
Vector, real with respect to an involution      91
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