Download or read book Hankel Operators on Hilbert Space written by S. C. Power and published by Pitman Publishing. This book was released on 1982 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book An Introduction to Hankel Operators written by Jonathan R. Partington and published by Cambridge University Press. This book was released on 1988 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hankel operators are of wide application in mathematics and engineering and this account of them is both elementary and rigorous.
Download or read book Hankel Operators and Their Applications written by Vladimir Peller and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 789 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this book is to describe the theory of Hankel operators, one of the most important classes of operators on spaces of analytic func tions. Hankel operators can be defined as operators having infinite Hankel matrices (i. e. , matrices with entries depending only on the sum of the co ordinates) with respect to some orthonormal basis. Finite matrices with this property were introduced by Hankel, who found interesting algebraic properties of their determinants. One of the first results on infinite Han kel matrices was obtained by Kronecker, who characterized Hankel matri ces of finite rank as those whose entries are Taylor coefficients of rational functions. Since then Hankel operators (or matrices) have found numerous applications in classical problems of analysis, such as moment problems, orthogonal polynomials, etc. Hankel operators admit various useful realizations, such as operators on spaces of analytic functions, integral operators on function spaces on (0,00), operators on sequence spaces. In 1957 Nehari described the bounded Hankel operators on the sequence space £2. This description turned out to be very important and started the contemporary period of the study of Hankel operators. We begin the book with introductory Chapter 1, which defines Hankel operators and presents their basic properties. We consider different realiza tions of Hankel operators and important connections of Hankel operators with the spaces BMa and V MO, Sz. -Nagy-Foais functional model, re producing kernels of the Hardy class H2, moment problems, and Carleson imbedding operators.
Download or read book Linear Systems and Operators in Hilbert Space written by Paul A. Fuhrmann and published by Courier Corporation. This book was released on 2014-02-19 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: A treatment of system theory within the context of finite dimensional spaces, this text is appropriate for students with no previous experience of operator theory. The three-part approach, with notes and references for each section, covers linear algebra and finite dimensional systems, operators in Hilbert space, and linear systems in Hilbert space. 1981 edition.
Download or read book An Introduction to Operators on the Hardy Hilbert Space written by Ruben A. Martinez-Avendano and published by Springer Science & Business Media. This book was released on 2007-03-12 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an elementary and engaging introduction to operator theory on the Hardy-Hilbert space. It provides a firm foundation for the study of all spaces of analytic functions and of the operators on them. Blending techniques from "soft" and "hard" analysis, the book contains clear and beautiful proofs. There are numerous exercises at the end of each chapter, along with a brief guide for further study which includes references to applications to topics in engineering.
Download or read book Hankel Operators on Hilbert Spaces written by Pachara Wanpen and published by . This book was released on 1993 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Operators Functions and Systems An Easy Reading written by Nikolai K. Nikolski and published by American Mathematical Soc.. This book was released on 2002 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Hankel Operators and Generalizations written by Ruben Alejandro Martinez Avendano and published by . This book was released on 2000 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Hankel Operators on Harmonic Bergman Spaces written by Mirjana Jovović and published by . This book was released on 1994 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Vectorial Hankel Operators with Toeplitz Weights written by Stephen Abbott and published by . This book was released on 1993 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Product and Commutation Properties of Hilbert Space Operators written by Michael John Hoffman and published by . This book was released on 1979 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Theory of H b Spaces Volume 1 written by Emmanuel Fricain and published by Cambridge University Press. This book was released on 2016-05-26 with total page 703 pages. Available in PDF, EPUB and Kindle. Book excerpt: An H(b) space is defined as a collection of analytic functions which are in the image of an operator. The theory of H(b) spaces bridges two classical subjects: complex analysis and operator theory, which makes it both appealing and demanding. The first volume of this comprehensive treatment is devoted to the preliminary subjects required to understand the foundation of H(b) spaces, such as Hardy spaces, Fourier analysis, integral representation theorems, Carleson measures, Toeplitz and Hankel operators, various types of shift operators, and Clark measures. The second volume focuses on the central theory. Both books are accessible to graduate students as well as researchers: each volume contains numerous exercises and hints, and figures are included throughout to illustrate the theory. Together, these two volumes provide everything the reader needs to understand and appreciate this beautiful branch of mathematics.
Download or read book An Introduction to Hilbert Space written by N. Young and published by Cambridge University Press. This book was released on 1988-07-21 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is an introduction to the theory of Hilbert space and its applications. The notion of Hilbert space is central in functional analysis and is used in numerous branches of pure and applied mathematics. Dr Young has stressed applications of the theory, particularly to the solution of partial differential equations in mathematical physics and to the approximation of functions in complex analysis. Some basic familiarity with real analysis, linear algebra and metric spaces is assumed, but otherwise the book is self-contained. It is based on courses given at the University of Glasgow and contains numerous examples and exercises (many with solutions). Thus it will make an excellent first course in Hilbert space theory at either undergraduate or graduate level and will also be of interest to electrical engineers and physicists, particularly those involved in control theory and filter design.
Download or read book Hankel Operators on the Drury Arveson Space written by James Allen Sunkes (III) and published by . This book was released on 2016 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Drury-Arveson space, initially introduced in the proof of a generalization of von Neumann's inequality, has seen a lot of research due to its intrigue as a Hilbert space of analytic functions. This space has been studied in the context of Besov-Sobolev spaces, Hilbert spaces with complete Nevanlinna Pick kernels, and Hilbert modules. More recently, McCarthy and Shalit have studied the connections between the Drury-Arveson space and Hilbert spaces of Dirichlet series, and Davidson and Cloutâre have established analogues of classic results of the ball algebra to the multiplier algebra for the Drury-Arveson Space. The goal of this dissertation is to contribute to this growing body of research by studying the Hankel operators on the Drury-Arveson Space. We begin by establishing basic results regarding the function theoretic properties of the Drury-Arveson space and general properties of Hankel operators. It is then shown that every invariant subspace of the d-shift on the Drury-Arveson space is an at most countable intersection of kernels of Hankel operators. We then prove that if a function and its reciprocal lie in the Drury-Arveson space, then that function must be a cyclic vector. In addition, we prove that each multiplier invariant subspace on the vector-valued Drury-Arveson space is an intersection of kernels of vectorial Hankel operators, and we characterize a special class of symbols which induce a bounded Hankel operator in terms of a Carleson measure condition on the symbol.
Download or read book Holomorphic Spaces written by Sheldon Jay Axler and published by Cambridge University Press. This book was released on 1998-05-28 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: Expository articles describing the role Hardy spaces, Bergman spaces, Dirichlet spaces, and Hankel and Toeplitz operators play in modern analysis.
Download or read book Operators Functions and Systems An Easy Reading written by Nikolai K. Nikolski and published by American Mathematical Soc.. This book was released on 2010-10-06 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Operator Theory in Function Spaces written by Kehe Zhu and published by American Mathematical Soc.. This book was released on 2007 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers Toeplitz operators, Hankel operators, and composition operators on both the Bergman space and the Hardy space. The setting is the unit disk and the main emphasis is on size estimates of these operators: boundedness, compactness, and membership in the Schatten classes. Most results concern the relationship between operator-theoretic properties of these operators and function-theoretic properties of the inducing symbols. Thus a good portion of the book is devoted to the study of analytic function spaces such as the Bloch space, Besov spaces, and BMOA, whose elements are to be used as symbols to induce the operators we study. The book is intended for both research mathematicians and graduate students in complex analysis and operator theory. The prerequisites are minimal; a graduate course in each of real analysis, complex analysis, and functional analysis should sufficiently prepare the reader for the book. Exercises and bibliographical notes are provided at the end of each chapter. These notes will point the reader to additional results and problems. Kehe Zhu is a professor of mathematics at the State University of New York at Albany. His previous books include Theory of Bergman Spaces (Springer, 2000, with H. Hedenmalm and B. Korenblum) and Spaces of Holomorphic Functions in the Unit Ball (Springer, 2005). His current research interests are holomorphic function spaces and operators acting on them.
