Spectral Theory Of Block Operator Matrices And Applications Christiane Tretter by Christiane Tretter 9781860947681, 1860947689 instant download after payment.

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; Special Classes of Block Operator Matrices; Spectral Inclusion; Estimates of the Resolvent; Corners of the Quadratic Numerical Range; Schur Complements and Their Factorization; Block Diagonalization; Spectral Supporting Subspaces; Variational Principles for Eigenvalues in Gaps; J-Self-Adjoint Block Operator Matrices; The Block Numerical Range; Numerical Ranges of Operator Polynomials; Gershgorin's Theorem for Block Operator Matrices; Unbounded Block Operator Matrices:; Relative Boundedness and Relative Compactness; Closedness and Closability of Block Operator Matrices; Spectrum and Resolvent; The Essential Spectrum; Spectral Inclusion; Symmetric and J-Symmetric Block Operator Matrices; Dichotomous Block Operator Matrices and Riccati Equations; Block Diagonalization and Half Range Completeness; Uniqueness Results for Solutions of Riccati Equations; Variational Principles; Eigenvalue Estimates; Applications in Mathematical Physics:; Upper Dominant Block Operator Matrices in Magnetohydrodynamics; Diagonally Dominant Block Operator Matrices in Fluid Mechanics; Off-Diagonally Dominant Block Operator Matrices in Quantum Mechanics