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Operator functions and localization of spectra / Michael I. Gil'.

By: Material type: TextTextSeries: Lecture notes in mathematics (Springer-Verlag) ; 1830.Publication details: Berlin ; New York : Springer-Verlag, ©2003.Description: 1 online resource (xiv, 256 pages) : illustrationsContent type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9783540452256
  • 3540452257
Subject(s): Additional physical formats: Print version:: Operator functions and localization of spectra.DDC classification:
  • 510 s 515/.7246 22
LOC classification:
  • QA3 .L28 no. 1830 QA329.2
Online resources:
Contents:
Preface -- Preliminaries -- Norms of Matrix-Valued Functions -- Invertibility of Finite Matrices -- Localization of Eigenvalues of Finite Matrices -- Block Matrices and pi-triangular Matrices -- Norm Estimates for Functions -- Functions of Non-Compact Operators -- Bounded Perturbations of Nonself-Adjoint Operators -- Spectrum Localization of Nonself-Adjoint Operators -- Multiplicative Representations of Resolvents -- Relatively $P$-triangular Operators -- Relatively Compact Perturbations of Normal Operators -- Infinite Matrices in Hilbert Spaces and Differential Operators -- Integral Operators in L2 -- Operator Matrices -- Hille -- Tamarkin Integral Operators -- Integral Operators in L8 -- Hille -- Tamarkin Matrices -- Zeros of Entire Functions -- List of Main Symbols -- Index.
Summary: "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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Includes bibliographical references and index.

Preface -- Preliminaries -- Norms of Matrix-Valued Functions -- Invertibility of Finite Matrices -- Localization of Eigenvalues of Finite Matrices -- Block Matrices and pi-triangular Matrices -- Norm Estimates for Functions -- Functions of Non-Compact Operators -- Bounded Perturbations of Nonself-Adjoint Operators -- Spectrum Localization of Nonself-Adjoint Operators -- Multiplicative Representations of Resolvents -- Relatively $P$-triangular Operators -- Relatively Compact Perturbations of Normal Operators -- Infinite Matrices in Hilbert Spaces and Differential Operators -- Integral Operators in L2 -- Operator Matrices -- Hille -- Tamarkin Integral Operators -- Integral Operators in L8 -- Hille -- Tamarkin Matrices -- Zeros of Entire Functions -- List of Main Symbols -- Index.

"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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