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基本説明
Includes many examples from applications to illustrate results.
Full Description
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; variational principles and eigenvalue estimates; block diagonalization and invariant subspaces; solutions of algebraic Riccati equations; applications to spectral problems from magnetohydrodynamics, fluid mechanics, and quantum mechanics.
Contents
Bounded Block Operator Matrices: The Quadratic Numerical Range; Spectral Inclusion; Estimates of the Resolvent; Corners of the Quadratic Numerical Range; Schur Complements and Their Factorization; Block Diagonalization; The Block Numerical Range; Numerical Rangs of Operator Polynomials and Block Numerical Ranges; Unbounded Block Operator Matrices: Closedness and Closability of Block Operator Matrices; Spectrum, Schur Complements and Quadratic Complements; Spectral Inclusion; Eigenvalues and Variational Principles; Solutions of Riccati Equations and Block Diagonalization; Applications in Mathematical Physics.
