Gil’ M.I. — Operator functions and localization of spectra :: Электронная библиотека попечительского совета мехмата МГУ

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Gil’ M.I. — Operator functions and localization of spectra

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Название: Operator functions and localization of spectra

Автор: Gil’ M.I.

Аннотация:

Operator Functions and Localization of Spectra is the first book that presents a systematic exposition of bounds for the spectra of various linear nonself-adjoint operators in a Hilbert space, having discrete and continuous spectra. In particular bounds for the spectra of integral, differential and integro-differential operators, as well as finite and infinite matrices are established. The volume also presents a systematic exposition of estimates for norms of operator-valued functions and their applications.

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Рубрика: Математика/Анализ/Продвинутый анализ/

Статус предметного указателя: Готов указатель с номерами страниц

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Год издания: 2003

Количество страниц: 260

Добавлена в каталог: 02.04.2005

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Предметный указатель

Carleman inequality      33 93
Diagonal part of compact operator      82
Diagonal part of matrix      8
Diagonal part of noncompact operator      99
Estimate for norm of function matrix      21
Estimate for norm of function of Hilbert — Schmidt operator      91
Estimate for norm of function quasi-Hermitian operator      110 113
Estimate for norm of function, quasiunitary operator      119
Estimate for norm of powers, finite nilpotent matrices      18 37
Estimate for norm of powers, Hilbert — Schmidt Volterra operator      92
Estimate for norm of powers, Neumann — Schatten Volterra operator      93
Estimate for norm of resolvent of Hilbert — Schmidt operator      83
Estimate for norm of resolvent of matrix      11
Estimate for norm of resolvent of Neumann — Schatten operator      88
Estimate for norm of resolvent of operators with Hilbert — Schmidt power      86
Estimate for norm of resolvent of quasi-Hermitian operator      106
Estimate for norm of resolvent of quasiunitary operator      118
Euclidean norm      1
Frobenius norm of matrix      2
Hausdorff distance between spectra      49 129
Hilbert — Schmidt ideal      78
Hilbert — Schmidt norm      2 78
Hilbert — Schmidt operator      78
Hille — Tamarkin integral operator      215
Hille — Tamarkin matrix      235
Lidskij’s theorem      79
Matrix-valued function      4
Maximal resolution of identity (m.r.i)      98
Multiplicative representation for resolvent of $\pi$ -triangular matrice      69
Multiplicative representation for resolvent of finite dimensional operators      24 27
Multiplicative representation for resolvent of operator in Hilbert space      151—160
Multiplicity of eigenvalue of matrix      3

Multiplicity of eigenvalue of operator in a Hilbert space      77
Neumann — Schatten ideal      78
Nilpotency index      102
Nilpotent part of compact operator      82
Nilpotent part of finite matrix      8
Nilpotent part of noncompact operator      99
Normal matrix      2
Normal operator      76
P-triangular operator      98
Positive selfadjoint operator      76
Quasi-Hermitian operator      98
Quasinilpotent operator      77
Quasinormal operator      98
Quasiunitary operator      116
Relative nilpotent part      164
Relative P-triangular operator      164
Relative spectral variation      167
Resolution of identity      98
Resolution of identity, maximal (m.r.i.)      98
Root vectors      77
Schur’s basis      7 81
Singular numbers of compact operators      78
Spectral variation      49 129
Trace class      78
Trace of linear operator      78
Trace of matrix      3
Triangular representation of compact operator      82
Triangular representation of matrix      7
Triangular representation of quasi-Hermitian operator      104
Triangular representation of quasiunitary operator      116
Triangular representation of regular function of operator      115
Unitary operator      76
Volterra operator      77

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