Model Operators and Systems PDF Download

Author: Nikolaj K. Nikol'skij
Publisher:
ISBN: 9780821828762
Category :
Languages : en
Pages : 439

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Author: Nikolai K. Nikolski
Publisher: American Mathematical Soc.
ISBN: 0821852655
Category : Control theory
Languages : en
Pages : 439

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Book Description
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.

Author: Nikolaĭ Kapitonovich Nikolʹskiĭ
Publisher: American Mathematical Society(RI)
ISBN: 9780821828762
Category : Control theory
Languages : en
Pages : 0

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Book Description
Overall, this work combines together - in two volumes - four formally distinct topics of modern analysis and their applications: Hardy classes of holomorphic functions; spectral theory of Hankel and Toeplitz operators; function models for linear operators and free interpolations; and infinite-dimensional system theory and signal processing. This, the second volume, contains parts C and D of the whole.

Author: Nikolaĭ Kapitonovich Nikolʹskiĭ
Publisher:
ISBN:
Category : Control theory
Languages : en
Pages : 439

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Book Description

Author: Nikolaĭ Kapitonovich Nikolʹskiĭ
Publisher: American Mathematical Soc.
ISBN: 9780821828762
Category : Control theory
Languages : en
Pages : 460

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Book Description

Author: Nikolaĭ Kapitonovich Nikolʹskiĭ
Publisher:
ISBN: 9781470413194
Category : MATHEMATICS
Languages : en
Pages : 479

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Book Description
One of two volumes, this text combines distinct topics of modern analysis and its applications: Hardy classes of holomorphic functions; spectral theory of Hankel and Toeplitz operators. Each topic has important implications for complex analysis.

Author: Jonathan R. Partington
Publisher: Cambridge University Press
ISBN: 9780521546195
Category : Mathematics
Languages : en
Pages : 184

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Publisher Description

Author: Nikolai K. Nikolski
Publisher: American Mathematical Soc.
ISBN: 0821849336
Category : Control theory
Languages : en
Pages : 482

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Book Description
One of two volumes, this text combines distinct topics of modern analysis and its applications: Hardy classes of holomorphic functions; spectral theory of Hankel and Toeplitz operators. Each topic has important implications for complex analysis.

Author: Joseph A. Ball
Publisher: Cambridge University Press
ISBN: 1009020102
Category : Mathematics
Languages : en
Pages : 440

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Book Description
This concise monograph explores how core ideas in Hardy space function theory and operator theory continue to be useful and informative in new settings, leading to new insights for noncommutative multivariable operator theory. Beginning with a review of the confluence of system theory ideas and reproducing kernel techniques, the book then covers representations of backward-shift-invariant subspaces in the Hardy space as ranges of observability operators, and representations for forward-shift-invariant subspaces via a Beurling–Lax representer equal to the transfer function of the linear system. This pair of backward-shift-invariant and forward-shift-invariant subspace form a generalized orthogonal decomposition of the ambient Hardy space. All this leads to the de Branges–Rovnyak model theory and characteristic operator function for a Hilbert space contraction operator. The chapters that follow generalize the system theory and reproducing kernel techniques to enable an extension of the ideas above to weighted Bergman space multivariable settings.

Author: Prof. Kevin F. Clancey
Publisher: Birkhäuser
ISBN: 3034854927
Category : Science
Languages : en
Pages : 246

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Book Description
A few years aga the authors started a project of a book on the theory of systems of one-dimensional singular integral equa tions which was planned as a continuation of the monograph by one of the authors and N. Ya. Krupnik ~~ concerning scalar equa tions. This set of notes was initiated as a chapter dealing with problems of factorization of matrix functions vis-a-vis appli cations to systems of singular integral equations. Working systematically onthischapter and adding along the way new points of view, new proofs and results, we finally saw that the material connected with factorizations is of independent interest and we decided to publish this chapter as aseparate volume. In fact, because of recent activity, the amount of material was quite large and we quickly learned that we cannot cover all of the results in complete detail. We have tried to include a represen tative variety of all kinds of methods, techniques,results and applications. Apart of the current work exposes results from the Russian literature which have never appeared in English translation. We have also decided to reflect some of the recent results which make interesting connections between factorization of matrix functions and systems theory. The field remains very active and many results and connec tions are still not weIl understood. These notes should be viewed as a stepping stone to further development. The authors hope that sometime they will return to complete their original plan.