Spectral Properties of Banded Toeplitz Matrices by Albrecht Böttcher (PDF)

Description

This self-contained introduction to the behavior of several spectral characteristics of large Toeplitz band matrices is the first systematic presentation of a relatively large body of knowledge, covering everything from classic results to the most recent developments. The spectral characteristics include determinants, eigenvalues and eigenvectors, pseudospectra and pseudomodes, singular values, norms, and condition numbers. Toeplitz matrices emerge in many applications and the literature on them is immense. They remain an active field of research with many facets, and the material on banded ones until now has primarily been found in research papers. The book may serve both as an introductory text and as a reference. The approach is based on the experience of the authors in combining functional analytical methods with hard analysis, and in applying operator theoretical methods to matrix theory, revealing the essence of several phenomena and leading to significant improvements in existing results.

User’s Reviews

Editorial Reviews: Review ‘This is a wonderful book, full of the latest material on Toeplitz matrices and operators, including norms, spectra, pseudospectra, fields of values, and polynomial hulls. The notes at the end of the chapters are especially interesting and the exercises are challenging. The writing is careful and precise but also entertaining.’ Anne Greenbaum, Professor of Mathematics, University of Washington’This book is a tremendous resource for all aspects of the spectral theory of banded Toeplitz matrices. It will be the first place I turn when looking for many results in this field, and given this book’s amazing breadth and depth, I expect to find just what I need.’ Mark Embree, Assistant Professor of Computational and Applied Mathematics, Rice University Book Description This is an introduction to the behavior of several spectral characteristics of large Toeplitz band matrices. Book Description This self-contained introduction to the behavior of several spectral characteristics of large Toeplitz band matrices is the first systematic presentation of a relatively large body of knowledge, covering everything from classic results to the most recent developments. It may serve both as an introductory text and as a reference. About the Author Albrecht Böttcher is Professor of Mathematics at Chemnitz University of Technology, Germany. He is author or coauthor of seven books and approximately 140 research papers, and he is on the editorial board of three mathematics journals and one book series. In 1992 he received the Alfried Krupp Award for Young University Teachers and in 1997 the Ferran Sunyer i Balaguer Prize. Sergei M. Grudsky is Professor of Mathematics at Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional (CINVESTAV del I.P.N.) in Mexico City and also Professor of Mathematics at the Faculty of Mechanics and Mathematics at Rostov-on-Don State University, Russia. He is author or coauthor of three books and approximately 80 research papers. Read more

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