Operators, functions and systems : an easy reading, Volume 2, model operators and systems / Nikolai K. Nikolski ; transl. by Andreas HartmannType de document : MonographieCollection : Mathematical surveys and monographs, 93Langue : anglais.Pays : Etats Unis.Éditeur : Providence : American Mathematical Society, 2002Description : 1 vol. (XIV-439 p.) : errata ; 26 cmISBN : 9780821828762.ISSN : 0885-4653.Bibliographie : Bibliogr. p. 361-400. 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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Bibliogr. p. 361-400. Index
Together with the companion volume by the same author, Operators, Functions, and Systems: An Easy Reading. Volume 1: Hardy, Hankel, and Toeplitz, Mathematical Surveys and Monographs, Vol. 92, 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 C and D.
Function models for linear operators and free interpolations: This is a universal topic and, indeed, is the most influential operator theory technique in the post-spectral-theorem era. In this book, its capacity is tested by solving generalized Carleson-type interpolation problems.
Infinite-dimensional system theory and signal processing: This topic is the touchstone of the three previously developed techniques. The presence of this applied topic in a pure mathematics environment reflects important changes in the mathematical landscape of the last 20 years, in that the role of the main consumer and customer of harmonic, complex, and operator analysis has more and more passed from differential equations, scattering theory, and probability to control theory and signal processing.
This and the companion volume are geared toward a wide audience of readers, from graduate students to professional mathematicians. They develop an elementary approach to the subject while retaining an expert level that can be applied in advanced analysis and selected applications. (source : AMS)