Ebook: Operator Functions and Localization of Spectra
Author: Michael I. Gil’ (auth.)
- Tags: Operator Theory, Linear and Multilinear Algebras Matrix Theory, Functions of a Complex Variable, Integral Equations
- Series: Lecture Notes in Mathematics 1830
- Year: 2003
- Publisher: Springer-Verlag Berlin Heidelberg
- Edition: 1
- Language: English
- pdf
"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.
"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.
"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.
Content:
1 Preliminaries....Pages 1-9
2 Norms of Matrix-Valued Functions....Pages 11-34
3 Invertibility of Finite Matrices....Pages 35-48
4 Localization of Eigenvalues of Finite Matrices....Pages 49-63
5 Block Matrices and ? -Triangular Matrices....Pages 65-74
6 Norm Estimates for Functions of Compact Operators in a Hilbert Space....Pages 75-96
7 Functions of Non-compact Operators....Pages 97-121
8 Bounded Perturbations of Nonselfadjoint Operators....Pages 123-134
9 Spectrum Localization of Nonself-adjoint Operators....Pages 135-149
10 Multiplicative Representations of Resolvents....Pages 151-161
11 Relatively P-Triangular Operators....Pages 163-172
12 Relatively Compact Perturbations of Normal Operators....Pages 173-180
13 Infinite Matrices in Hilbert Spaces and Differential Operators....Pages 181-188
14 Integral Operators in Space L 2 ....Pages 189-197
15 Operator Matrices....Pages 199-213
16 Hille - Tamarkin Integral Operators....Pages 215-226
17 Integral Operators in Space L ? ....Pages 227-234
18 Hille - Tamarkin Matrices....Pages 235-241
19 Zeros of Entire Functions....Pages 243-252
"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.
Content:
1 Preliminaries....Pages 1-9
2 Norms of Matrix-Valued Functions....Pages 11-34
3 Invertibility of Finite Matrices....Pages 35-48
4 Localization of Eigenvalues of Finite Matrices....Pages 49-63
5 Block Matrices and ? -Triangular Matrices....Pages 65-74
6 Norm Estimates for Functions of Compact Operators in a Hilbert Space....Pages 75-96
7 Functions of Non-compact Operators....Pages 97-121
8 Bounded Perturbations of Nonselfadjoint Operators....Pages 123-134
9 Spectrum Localization of Nonself-adjoint Operators....Pages 135-149
10 Multiplicative Representations of Resolvents....Pages 151-161
11 Relatively P-Triangular Operators....Pages 163-172
12 Relatively Compact Perturbations of Normal Operators....Pages 173-180
13 Infinite Matrices in Hilbert Spaces and Differential Operators....Pages 181-188
14 Integral Operators in Space L 2 ....Pages 189-197
15 Operator Matrices....Pages 199-213
16 Hille - Tamarkin Integral Operators....Pages 215-226
17 Integral Operators in Space L ? ....Pages 227-234
18 Hille - Tamarkin Matrices....Pages 235-241
19 Zeros of Entire Functions....Pages 243-252
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