Operator Functions and Localization of Spectra

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.

List of 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.

Product details

• Authors: Michael I. Gil, Michael I. Gil'
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 17.11.2003
• EAN: 9783540202462
• ISBN: 978-3-540-20246-2
• No. of pages: 262
• Dimensions: 153 mm x 236 mm x 17 mm
• Weight: 416 g
• Illustrations: XIV, 262 p.
• Series: Lecture Notes in Mathematics
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Analysis; Algebra, B, Integralrechnung und -gleichungen, Komplexe Analysis, komplexe Variablen, Funktionentheorie, Mathematics and Statistics, Linear Algebra, Complex analysis, complex variables, Integral calculus & equations, Matrix theory, Linear and Multilinear Algebras, Matrix Theory, Integral Equations, Operator Theory, Functions of a Complex Variable, Functions of complex variables