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AuthorBรถttcher, Albrecht. author
TitleAnalysis of Toeplitz Operators [electronic resource] / by Albrecht Bรถttcher, Bernd Silbermann
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1990
Connect tohttp://dx.doi.org/10.1007/978-3-662-02652-6
Descript 512 p. online resource

SUMMARY

This book was originally intended as an extended version of our book "Invertibility and Asymptotics of Toeplitz Matrices", which appeared in 1983. We planned to discuss several topics in more detail, but our main concern was to incorporate a whole series of new results obtained during the last few years. However, we soon realized that the program we had in mind required new thoughts from both the methodological and substantial point of view, and so we decided to attempt writing a completely new book on the analysis of Toeplitz operators. There are at least two reasons for the continuous and increasing interest in Toeplitz operators. On the one hand, Toeplitz operators are of importance in connection with a variety of problems in physics, probability theory, information and control theory, and several other fields. Although we shall not embark on these problems, the selection of the material of this book is to a certain extent determined by such applications. On the other hand, besides the differential operators, Toeplitz operators constitute one of the most important classes of non-selfadjoint operators and they are a fascinating example of the fruitful interplay between such topics as operator theory, function theory, and the theory of Banach algebras. One main purpose of this book is to elucidate some of the ideas and methods illustrating just the latter aspect


CONTENT

1. Auxiliary material -- 2. Basic theory -- 3. Symbol analysis -- 4. Toeplitz operators on H2 -- 5. Toeplitz operators on Hp -- 6. Toeplitz operators on lp -- 7. Finite section method -- 8. Toeplitz operators over the quarter-plane -- 9. Wiener-Hopf integral operators -- 10. Toeplitz determinants -- References -- Notation index -- Name index


Mathematics Mathematical analysis Analysis (Mathematics) Numerical analysis Physics Statistics Mathematics Analysis Numerical Analysis Statistics general Theoretical Mathematical and Computational Physics



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