Spectral theory of block operator matrices and applications / Christiane Tretter.

Format:

Book

Author/Creator:

Tretter, Christiane.

Language:

English

Subjects (All):

Operator theory.

Matrices.

Spectral theory (Mathematics).

Physical Description:

1 online resource (296 p.)

Edition:

1st ed.

Place of Publication:

London : Imperial College Press ; Singapore ; Hackensack, NJ : Distributed by World Scientific Pub., c2008.

Language Note:

English

Summary:

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: non-self-adjoint block operator matrices, block operator matrices with unbounded entries, non-semibounded block operator matrices, and classes of block operator matrices arising in mathematical physics.The main topics include: localization of the spectrum by means of new concepts of numerical range; investigation of the essential spectrum; variation

Contents:

Preface; Introduction; Contents; 1. Bounded Block Operator Matrices; 1.1 The quadratic numerical range; 1.2 Special classes of block operator matrices; 1.3 Spectral inclusion; 1.4 Estimates of the resolvent; 1.5 Corners of the quadratic numerical range; 1.6 Schur complements and their factorization; 1.7 Block diagonalization; 1.8 Spectral supporting subspaces; 1.9 Variational principles for eigenvalues in gaps; 1.10 J -self-adjoint block operator matrices; 1.11 The block numerical range; 1.12 Numerical ranges of operator polynomials; 1.13 Gershgorin's theorem for block operator matrices

2. Unbounded Block Operator Matrices 2.1 Relative boundedness and relative compactness; 2.2 Closedness and closability of block operator matrices; 2.3 Spectrum and resolvent; 2.4 The essential spectrum; 2.5 Spectral inclusion; 2.6 Symmetric and J -symmetric block operator matrices; 2.7 Dichotomous block operator matrices and Riccati equations; 2.7.1 Essentially self-adjoint block operator matrices; 2.7.2 Non-self-adjoint block operator matrices; 2.8 Block diagonalization and half range completeness; 2.9 Uniqueness results for solutions of Riccati equations; 2.10 Variational principles

2.11 Eigenvalue estimates 3. Applications in Mathematical Physics; 3.1 Upper dominant block operator matrices in magnetohydrodynamics; 3.2 Diagonally dominant block operator matrices in uid mechanics; 3.3 O -diagonally dominant block operator matrices in quantum mechanics; 3.3.1 Dirac operators in R3; 3.3.2 The angular part of the Dirac equation in the Kerr-Newman metric; Bibliography; Index

Notes:

Description based upon print version of record.

Includes bibliographical references (p. 239-260) and index.

ISBN:

9781848161122

1848161123

OCLC:

830324576