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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: 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. ## About book:

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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;

- Author:
**Christiane Tretter** - Year:
**2008** - Publisher:
**Imperial College Press** - Language:
**English** - ISBN:
**1-86094-768-9,978-1-86094-768-1**

- File size:
**4 506 026** - Format:
**pdf**

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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: no...

The present volume is the first of two volumes containing a collection of original and review articles on recent advances and new directions in a multifaceted and interconnected area of mathematics and its applications. It encompasses many topics in theor...

The spectral theory of Sturm-Liouville operators is a classical domain of analysis, comprising a wide variety of problems. Besides the basic results on the structure of the spectrum and the eigenfunction expansion of regular and singular Sturm-Liouville p...

The spectral theory of ordinary differential operators L and of the equations (0.1) Ly= AY connected with such operators plays an important role in a number of problems both in physics and in mathematics. Let us give some examples of differential operator...

Spectral theory for linear operators has become an important part of functional analysis and operator theory. This text seeks to define a spectrum for nonlinear operators that preserves the useful properties of the linear case, but permits broader applica...

Providing a basic tool for studying nonlinear problems, Spectral Theory for Random and Nonautonomous Parabolic Equations and Applications focuses on the principal spectral theory for general time-dependent and random parabolic equations and systems. The ...

The main aim of this book is to introduce the reader to the concept of comparison algebra, defined as a type of C*-algebra of singular integral operators. The first part of the book develops the necessary elements of the spectral theory of differential op...

This EMS volume contains a survey of the principles and advanced techniques of the spectral theory of linear differential and pseudodifferential operators in finite-dimensional spaces. Also including a special section of Sunada's recent solution of Kac's ...

This textbook provides an introduction to the new techniques of subharmonic functions and analytic multifunctions in spectral theory. Topics include the basic results of functional analysis, bounded operations on Banach and Hilbert spaces, Banach algebras...

Building contract claims for more time on projects represent one of the largest sources of dispute within the industry. However, identifying the causes of delays, and the effects they have on the project, is often difficult and the burden on the party see...

The papers collected here are, with three exceptions, those presented at a conference on probability and causation held at the University of California at Irvine on July 15-19, 1985. The exceptions are that David Freedman and Abner Shimony were not able t...

The European Organization for Cooperation in Cancer Prevention Studies (ECP) was established in 1981 to promote collaboration between scientists working in the various European countries on cancer causation and prevention. In order to achieve this aim, va...

All humans eventually die, but life expectancies differ over time and among different demographic groups. Teasing out the various causes and correlates of death is a challenge, and it is one we take on in this book. A look at the data on mortality is both...

Causation and Laws of Nature is a collection of articles which represents current research on the metaphysics of causation and laws of nature, mostly by authors working in or active in the Australasian region. The book provides an overview of current work...

Causes and Control of Colorectal Cancer: A Model for Cancer Prevention is a ground- breaking monograph which takes a global, multidisciplinary approach to the causes, carcinogenesis and control of colorectal cancer. Over 1000 key studies were analyzed on ...

Arturo Carsetti According to molecular Biology, true invariance (life) can exist only within the framework of ongoing autonomous morphogenesis and vice versa. With respect to this secret dialectics, life and cognition appear as indissolubly interlinked. I...

Introduces graduate students and researchers to mathematical physics, providing a mathematical discourse on the relation between theoretical and experimental physics....