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Operators, functions and systems : an easy reading, Volume 1, Hardy, Hankel, and Toeplitz / Nikolai K. Nikolski ; transl. by Andreas Hartmann

Auteur principal : Nikolski, Nikolai Kapitonovitch, 1940-, AuteurAuteur secondaire : Hartmann, Andreas, TraducteurType de document : MonographieCollection : Mathematical surveys and monographs, 92Langue : anglais.Pays : Etats Unis.Éditeur : Providence : American Mathematical Society, 2002Description : 1 vol. (XIV-461 p.) ; 26 cmISBN : 9780821810835.ISSN : 0885-4653.Bibliographie : Bibliogr. p. 401-440. Index.Sujet MSC : 47A40, Operator theory -- General theory of linear operators, Scattering theory
47A57, Operator theory -- General theory of linear operators, Operator methods in interpolation, moment and extension problems
47A45, Operator theory -- General theory of linear operators, Canonical models for contractions and nonselfadjoint operators
47B35, Operator theory -- Special classes of linear operators, Toeplitz operators, Hankel operators, Wiener-Hopf operators
43A15, Abstract harmonic analysis -- Abstract harmonic analysis, Lp-spaces and other function spaces on groups, semigroups, etc.
En-ligne : Zentralblatt | MathSciNet | AMS
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Contient des exercices

Bibliogr. p. 401-440. Index

Together with the companion volume by the same author, Operators, Functions, and Systems: An Easy Reading. Volume 2: Model Operators and Systems, Mathematical Surveys and Monographs, Vol. 93, AMS, 2002, this unique work combines four major topics of modern analysis and its applications:

A. Hardy classes of holomorphic functions,

B. Spectral theory of Hankel and Toeplitz operators,

C. Function models for linear operators and free interpolations, and

D. Infinite-dimensional system theory and signal processing.

This volume contains Parts A and B.

Hardy classes of holomorphic functions is known to be the most powerful tool in complex analysis for a variety of applications, starting with Fourier series, through the Riemann ζ-function, all the way to Wiener's theory of signal processing.

Spectral theory of Hankel and Toeplitz operators becomes the supporting pillar for a large part of harmonic and complex analysis and for many of their applications. In this book, moment problems, Nevanlinna-Pick and Carathéodory interpolation, and the best rational approximations are considered to illustrate the power of Hankel and Toeplitz operators.

The book is geared toward a wide audience of readers, from graduate students to professional mathematicians, interested in operator theory and functions of a complex variable. The two volumes develop an elementary approach while retaining an expert level that can be applied in advanced analysis and selected applications. (source : AMS)

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