Spectral Theory of Block Operator Matrices and Applications

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ISBN: 9781860947681 | 1860947689
Cover: Hardcover
Copyright: 12/31/2008

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"This book presents a wide panorama of methods to investigate the spectral properties of block operator matrices. Particular emphasis is placed on classes of block operator matrices to which standard operator theoretical methods do not readily apply: nonselfadjoint block operator matrices, block operator matrices with unbounded entries, non-semibounded block operator matrices, and classes of block operator matrices arising in mathematical physics."--BOOK JACKET.

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Bounded Block Operator Matrices	p. 1
The Quadratic Numerical Range	p. 1
Special Classes of Block Operator Matrices	p. 11
Spectral Inclusion	p. 18
Estimates of the Resolvent	p. 26
Corners of the Quadratic Numerical Range	p. 29
Schur Complements and Their Factorization	p. 35
Block Diagonalization	p. 42
Spectral Supporting Subspaces	p. 47
Variational Principles for Eigenvalues in Gaps	p. 59
J-Self-Adjoint Block Operator Matrices	p. 62
The Block Numerical Range	p. 70
Numerical Ranges of Operator Polynomials	p. 82
Gershgorin's Theorem for Block Operator Matrices	p. 86
Unbounded Block Operator Matrices	p. 91
Relative Boundedness and Relative Compactness	p. 91
Closedness and Closability of Block Operator Matrices	p. 99
Spectrum and Resolvent	p. 111
The Essential Spectrum	p. 116
Spectral Inclusion	p. 129
Symmetric and J-Symmetric Block Operator Matrices	p. 142
Dichotomous Block Operator Matrices and Riccati Equations	p. 154
Block Diagonalization and Half Range Completeness	p. 174
Uniqueness Results for Solutions of Riccati Equations	p. 180
Variational Principles	p. 193
Eigenvalue Estimates	p. 205
Applications in Mathematical Physics	p. 217
Upper Dominant Block Operator Matrices in Magnetohydrodynamics	p. 217
Diagonally Dominant Block Operator Matrices in Fluid Mechanics	p. 222
Off-Diagonally Dominant Block Operator Matrices in Quantum Mechanics	p. 227
Bibliography	p. 239
Index	p. 261
Table of Contents provided by Blackwell. All Rights Reserved.

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Spectral Theory of Block Operator Matrices and Applications

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