Toeplitz Matrices and Operators

Nikolaï Nikolski (Université de Bordeaux), Danièle Gibbons, Greg Gibbons

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English

Cambridge University Press
02 January 2020

Real analysis, real variables; Complex analysis, complex variables; Numerical analysis

Series: Cambridge Studies in Advanced Mathematics

The theory of Toeplitz matrices and operators is a vital part of modern analysis, with applications to moment problems, orthogonal polynomials, approximation theory, integral equations, bounded- and vanishing-mean oscillations, and asymptotic methods for large structured determinants, among others. This friendly introduction to Toeplitz theory covers the classical spectral theory of Toeplitz forms and Wiener–Hopf integral operators and their manifestations throughout modern functional analysis. Numerous solved exercises illustrate the results of the main text and introduce subsidiary topics, including recent developments. Each chapter ends with a survey of the present state of the theory, making this a valuable work for the beginning graduate student and established researcher alike. With biographies of the principal creators of the theory and historical context also woven into the text, this book is a complete source on Toeplitz theory.

By: Nikolaï Nikolski (Université de Bordeaux)
Translated by: Danièle Gibbons, Greg Gibbons
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Dimensions: Height: 235mm, Width: 156mm, Spine: 29mm
Weight: 750g
ISBN: 9781107198500
ISBN 10: 110719850X
Series: Cambridge Studies in Advanced Mathematics
Pages: 450
Publication Date: 02 January 2020
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

Nikolaï Nikolski is Professor Emeritus at the Université de Bordeaux, working primarily in analysis and operator theory. He has been co-editor of four international journals, editor of more than fifteen books, and published numerous articles and research monographs. He has also supervised twenty-six Ph.D. students, including three Salem Prize winners. Professor Nikolski was elected Fellow of the American Mathematical Society (AMS) in 2013 and received the Prix Ampère of the French Academy of Sciences in 2010.

Reviews for Toeplitz Matrices and Operators

'The author's love for all facets of the topic and his distinctive sense for culture and history resulted in a book of unique charm. The reader will enjoy a captivating journey from the historical roots up to the latest achievements of a fascinating field of concrete operator theory. An excellent source and a true treat for both beginners and professionals!' Albrecht Boettcher, Technische Universitat Chemnitz, Germany `The author's love for all facets of the topic and his distinctive sense for culture and history resulted in a book of unique charm. The reader will enjoy a captivating journey from the historical roots up to the latest achievements of a fascinating field of concrete operator theory. An excellent source and a true treat for both beginners and professionals!' Albrecht Boettcher, Technische Universitat Chemnitz, Germany