Treatise On The Shift Operator

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Treatise On The Shift Operator

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Author : N.K. Nikol'skii
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Treatise On The Shift Operator written by N.K. Nikol'skii and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

This book is an elementary introduction to non-classical spectral theory. Mter the basic definitions and a reduction to the study of the functional model the discussion will be centered around the simplest variant of such a model which, formally speaking, comprises only the class of contraction operators with a one dimensional rank of non-unitarity (rank(I - T*T) = rank(I - TT*) = 1). The main emphasis is on the technical side of the subject, the book being mostly devoted to a development of the analytical machinery of spectral theory rather than to this discipline itself. The functional model of Sz. -Nagy and Foia§ re duces the study of general operators to an investigation of the . compression T=PSIK of the shift operator S, Sf = zf, onto coinvariant subspaces (i. e. subspaces in variant with respect to the adjoint shift S*). In the main body of the book (the "Lectures" in the proper meaning of the word) this operator acts on the Hardy space H2 and is itself a part of the operator of multiplication by the independent variable in the space L2 (in the case at hand L2 means L2(lf), If being the unit circle), this operator again being fundamental for classical spectral theory.

Treatise On The Shift Operator

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Author : Nikol'skii Nikolai Kapitonovich
language : en
Publisher:
Release Date : 1986

Treatise On The Shift Operator written by Nikol'skii Nikolai Kapitonovich and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with categories.

Invariant Subspaces Of The Shift Operator

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Author : Javad Mashreghi
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-04-23

Invariant Subspaces Of The Shift Operator written by Javad Mashreghi and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-04-23 with Mathematics categories.

This volume contains the proceedings of the CRM Workshop on Invariant Subspaces of the Shift Operator, held August 26-30, 2013, at the Centre de Recherches Mathématiques, Université de Montréal, Montréal, Quebec, Canada. The main theme of this volume is the invariant subspaces of the shift operator (or its adjoint) on certain function spaces, in particular, the Hardy space, Dirichlet space, and de Branges-Rovnyak spaces. These spaces, and the action of the shift operator on them, have turned out to be a precious tool in various questions in analysis such as function theory (Bieberbach conjecture, rigid functions, Schwarz-Pick inequalities), operator theory (invariant subspace problem, composition operator), and systems and control theory. Of particular interest is the Dirichlet space, which is one of the classical Hilbert spaces of holomorphic functions on the unit disk. From many points of view, the Dirichlet space is an interesting and challenging example of a function space. Though much is known about it, several important open problems remain, most notably the characterization of its zero sets and of its shift-invariant subspaces. This book is co-published with the Centre de Recherches Mathématiques.

Linear Functional Equations Operator Approach

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Author : Anatolij Antonevich
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06

Linear Functional Equations Operator Approach written by Anatolij Antonevich and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

In this book we shall study linear functional equations of the form m bu(x) == Lak(X)U(Qk(X)) = f(x), (1) k=l where U is an unknown function from a given space F(X) of functions on a set X, Qk: X -+ X are given mappings, ak and f are given functions. Our approach is based on the investigation of the operators given by the left-hand side of equa tion (1). In what follows such operators will be called functional operators. We will pay special attention to the spectral properties of functional operators, first of all, to invertibility and the Noether property. Since the set X, the space F(X), the mappings Qk and the coefficients ak are arbitrary, the class of operators of the form (1) is very rich and some of its individ ual representatives are related with problems arising in various areas of mathemat ics and its applications. In addition to the classical theory of functional equations, among such areas one can indicate the theory of functional-differential equations with deviating argument, the theory of nonlocal problems for partial differential equations, the theory of boundary value problems for the equation of a vibrating string and equations of mixed type, a number of problems of the general theory of operator algebras and the theory of dynamical systems, the spectral theory of au tomorphisms of Banach algebras, and other problems.

Operators Functions And Systems An Easy Reading

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Author : Nikolai K. Nikolski
language : en
Publisher: American Mathematical Soc.
Release Date : 2010-10-06

Operators Functions And Systems An Easy Reading written by Nikolai K. Nikolski and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-10-06 with Mathematics categories.

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.

Toeplitz Operators And Spectral Function Theory

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Author : N. Nikolsky
language : en
Publisher: Birkhäuser
Release Date : 2013-12-01

Toeplitz Operators And Spectral Function Theory written by N. Nikolsky and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-01 with Social Science categories.

The volume contains selected papers of the Spectral Function Theory seminar, Leningrad Branch of Steklov Mathematical Institute. The papers are mostly devoted to the theory of Toeplitz and model operators. These subjects are considered here from various points of view. Several papers concern the relationships of Toeplitz operators to weighted polynomial approximation. Namely, two papers by B. Solomyak and A. Volberg intensively treat the problem of spectra! multiplicity f~r analytic Toeplitz operators (which are, in fact, multiplication operators) and my paper can serve as an introduction to the problem. This theme of multiplicities is continued in a paper by V. Vasyunin where the multiplicity of the spectrum is computed for Hilbert space contractions with finite defect indices. V. Peller's paper deals with a perturbation theory problem for Toeplitz operators. In a paper by D. Yakubovich a new similarity model for a class of Toeplitz operators is constructed. S. Treil' presents a survey of a part of spectral function theory for vector valued function (Szego-Kolmogorov extreme prob!ems for operator weights, bases of vector rational functions, estimations of Hilbert transform with respect to operator weights, the operator corona problem). As a concluding remark I dare only note that the whole collection convinces us once more without a doubt of the fruitfullness of the natural union of operator theory and complex analysis (if at all the union of these fields is at all different from their intersection).

Analysis Of Toeplitz Operators

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Author : A. Böttcher
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 1989-12-31

Analysis Of Toeplitz Operators written by A. Böttcher and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-12-31 with Mathematics categories.

No detailed description available for "Analysis of Toeplitz Operators".

Analysis Of Toeplitz Operators

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Author : Albrecht Böttcher
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29

Analysis Of Toeplitz Operators written by Albrecht Böttcher and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.

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, besidesthe 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.

Observation And Control For Operator Semigroups

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Author : Marius Tucsnak
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-03-13

Observation And Control For Operator Semigroups written by Marius Tucsnak and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-03-13 with Mathematics categories.

This book studies observation and control operators for linear systems where the free evolution of the state can be described by an operator semigroup on a Hilbert space. It includes a large number of examples coming mostly from partial differential equations.

Operator Theory And Its Applications

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Author : Alexander G. Ramm
language : en
Publisher: American Mathematical Soc.
Release Date : 2000

Operator Theory And Its Applications written by Alexander G. Ramm and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.

Together with the papers on the abstract operator theory are many papers on the theory of differential operators, boundary value problems, inverse scattering and other inverse problems, and on applications to biology, chemistry, wave propagation, and many other areas."--BOOK JACKET.