Download or read book Sub Hardy Hilbert Spaces in the Unit Disk written by Donald Sarason and published by Wiley-Interscience. This book was released on 1994-09-16 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: This up-to-date account brings together results previously scattered throughout the literature as well as new material in the area of function theory. The focus is on describing some of what has been learned thus far about the structure of the de Branges-Rovnyak spaces and their function-theoretic connections.
Download or read book Some Notes on the Theory of Hilbert Spaces of Analytic Functions of the Unit Disc written by Jorge-Nuno O. Silva and published by Universal-Publishers. This book was released on 1998-06 with total page 31 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this work we explore the relation between some local Dirichlet spaces and some operator ranges. As an application we give numerical bounds for an equivalence of norms on a particular subspace of the Hardy space. Based on these results we introduce an operator on H^2 which we study in some detail. We also introduce a Hilbert space of analytic functions on the unit disc, prove the polynomials are dense in it, and give a characterization of its elements. On these spaces we study the action of composition operators induced by holomorphic self maps of the disc. We give characterizations of the bounded and compact ones in terms of the behavior of the inducing maps.
Download or read book Pick Interpolation and Hilbert Function Spaces written by Jim Agler and published by American Mathematical Society. This book was released on 2023-02-22 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book first rigorously develops the theory of reproducing kernel Hilbert spaces. The authors then discuss the Pick problem of finding the function of smallest $H^infty$ norm that has specified values at a finite number of points in the disk. Their viewpoint is to consider $H^infty$ as the multiplier algebra of the Hardy space and to use Hilbert space techniques to solve the problem. This approach generalizes to a wide collection of spaces. The authors then consider the interpolation problem in the space of bounded analytic functions on the bidisk and give a complete description of the solution. They then consider very general interpolation problems. The book includes developments of all the theory that is needed, including operator model theory, the Arveson extension theorem, and the hereditary functional calculus.
Download or read book Hilbert Spaces of Analytic Functions written by Javad Mashreghi and published by American Mathematical Soc.. This book was released on 2010-01-01 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Hardy Spaces written by Nikolaï Nikolski and published by Cambridge University Press. This book was released on 2019-01-31 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of Hardy spaces is a cornerstone of modern analysis. It combines techniques from functional analysis, the theory of analytic functions and Lesbesgue integration to create a powerful tool for many applications, pure and applied, from signal processing and Fourier analysis to maximum modulus principles and the Riemann zeta function. This book, aimed at beginning graduate students, introduces and develops the classical results on Hardy spaces and applies them to fundamental concrete problems in analysis. The results are illustrated with numerous solved exercises that also introduce subsidiary topics and recent developments. The reader's understanding of the current state of the field, as well as its history, are further aided by engaging accounts of important contributors and by the surveys of recent advances (with commented reference lists) that end each chapter. Such broad coverage makes this book the ideal source on Hardy spaces.
Download or read book Toeplitz Approach to Problems of the Uncertainty Principle written by Alexei Poltoratski and published by American Mathematical Soc.. This book was released on 2015-03-07 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Uncertainty Principle in Harmonic Analysis (UP) is a classical, yet rapidly developing, area of modern mathematics. Its first significant results and open problems date back to the work of Norbert Wiener, Andrei Kolmogorov, Mark Krein and Arne Beurling. At present, it encompasses a large part of mathematics, from Fourier analysis, frames and completeness problems for various systems of functions to spectral problems for differential operators and canonical systems. These notes are devoted to the so-called Toeplitz approach to UP which recently brought solutions to some of the long-standing problems posed by the classics. After a short overview of the general area of UP the discussion turns to the outline of the new approach and its results. Among those are solutions to Beurling's Gap Problem in Fourier analysis, the Type Problem on completeness of exponential systems, a problem by Pólya and Levinson on sampling sets for entire functions, Bernstein's problem on uniform polynomial approximation, problems on asymptotics of Fourier integrals and a Toeplitz version of the Beurling-Malliavin theory. One of the main goals of the book is to present new directions for future research opened by the new approach to the experts and young analysts. A co-publication of the AMS and CBMS.
Download or read book The Cauchy Transform written by Joseph A. Cima and published by American Mathematical Soc.. This book was released on 2006 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Cauchy transform of a measure on the circle is a subject of both classical and current interest with a sizable literature. This book is a thorough, well-documented, and readable survey of this literature and includes full proofs of the main results of the subject. This book also covers more recent perturbation theory as covered by Clark, Poltoratski, and Aleksandrov and contains an in-depth treatment of Clark measures.
Download or read book Catherine Beneteau Alberto A Condori Constanze Liaw William T Ross and Alan A Sola written by Catherine Bénéteau: and published by American Mathematical Soc.. This book was released on 2016-12-22 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the Proceedings of the Conference on Completeness Problems, Carleson Measures, and Spaces of Analytic Functions, held from June 29–July 3, 2015, at the Institut Mittag-Leffler, Djursholm, Sweden. The conference brought together experienced researchers and promising young mathematicians from many countries to discuss recent progress made in function theory, model spaces, completeness problems, and Carleson measures. This volume contains articles covering cutting-edge research questions, as well as longer survey papers and a report on the problem session that contains a collection of attractive open problems in complex and harmonic analysis.
Download or read book Operator Theory And Analysis Of Infinite Networks written by Palle Jorgensen and published by World Scientific. This book was released on 2023-03-21 with total page 449 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume considers resistance networks: large graphs which are connected, undirected, and weighted. Such networks provide a discrete model for physical processes in inhomogeneous media, including heat flow through perforated or porous media. These graphs also arise in data science, e.g., considering geometrizations of datasets, statistical inference, or the propagation of memes through social networks. Indeed, network analysis plays a crucial role in many other areas of data science and engineering. In these models, the weights on the edges may be understood as conductances, or as a measure of similarity. Resistance networks also arise in probability, as they correspond to a broad class of Markov chains.The present volume takes the nonstandard approach of analyzing resistance networks from the point of view of Hilbert space theory, where the inner product is defined in terms of Dirichlet energy. The resulting viewpoint emphasizes orthogonality over convexity and provides new insights into the connections between harmonic functions, operators, and boundary theory. Novel applications to mathematical physics are given, especially in regard to the question of self-adjointness of unbounded operators.New topics are covered in a host of areas accessible to multiple audiences, at both beginning and more advanced levels. This is accomplished by directly linking diverse applied questions to such key areas of mathematics as functional analysis, operator theory, harmonic analysis, optimization, approximation theory, and probability theory.
Download or read book Quadrature Domains and Their Applications written by Peter Ebenfelt and published by Springer Science & Business Media. This book was released on 2006-03-10 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quadrature domains were singled out about 30 years ago by D. Aharonov and H.S. Shapiro in connection with an extremal problem in function theory. Since then, a series of coincidental discoveries put this class of planar domains at the center of crossroads of several quite independent mathematical theories, e.g., potential theory, Riemann surfaces, inverse problems, holomorphic partial differential equations, fluid mechanics, operator theory. The volume is devoted to recent advances in the theory of quadrature domains, illustrating well the multi-facet aspects of their nature. The book contains a large collection of open problems pertaining to the general theme of quadrature domains.
Download or read book A Panorama of Modern Operator Theory and Related Topics written by Harry Dym and published by Springer Science & Business Media. This book was released on 2012-02-01 with total page 635 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is dedicated to the memory of Israel Gohberg (1928–2009) – one of the great mathematicians of our time – who inspired innumerable fellow mathematicians and directed many students. The volume reflects the wide spectrum of Gohberg’s mathematical interests. It consists of more than 25 invited and peer-reviewed original research papers written by his former students, co-authors and friends. Included are contributions to single and multivariable operator theory, commutative and non-commutative Banach algebra theory, the theory of matrix polynomials and analytic vector-valued functions, several variable complex function theory, and the theory of structured matrices and operators. Also treated are canonical differential systems, interpolation, completion and extension problems, numerical linear algebra and mathematical systems theory.
Download or read book Recent Progress in Operator Theory and Its Applications written by Joseph A. Ball and published by Springer Science & Business Media. This book was released on 2012-02-24 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains twenty-one solicited articles by speakers at the IWOTA 2009 workshop, ranging from expository surveys to original research papers, each carefully refereed. The contributions reflect recent developments in operator theory and its applications. Consistent with the topics of recent IWOTA meetings, IWOTA 2009 was designed as a comprehensive, inclusive conference covering all aspects of theoretical and applied operator theory, ranging from classical analysis, differential and integral equations, complex and harmonic analysis to mathematical physics, mathematical systems and control theory, signal processing and numerical analysis. The conference brought together international experts for a week-long stay at Hotel Real de Minas, in an atmosphere conducive to fruitful professional interactions. These Proceedings reflect the high quality of the papers presented at the conference.
Download or read book Recent Advances in Operator Related Function Theory written by Alec L. Matheson and published by American Mathematical Soc.. This book was released on 2006 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: The articles in this book are based on talks at a conference devoted to interrelations between function theory and the theory of operators. The main theme of the book is the role of Alexandrov-Clark measures. Two of the articles provide the introduction to the theory of Alexandrov-Clark measures and to its applications in the spectral theory of linear operators. The remaining articles deal with recent results in specific directions related to the theme of the book.
Download or read book Systems Approximation Singular Integral Operators and Related Topics written by Alexander A. Borichev and published by Birkhäuser. This book was released on 2012-12-06 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to some topical problems and applications of operator theory and its interplay with modern complex analysis. It consists of 20 selected survey papers that represent updated (mainly plenary) addresses to the IWOTA 2000 conference held at Bordeaux from June 13 to 16, 2000. The main subjects of the volume include: - spectral analysis of periodic differential operators and delay equations, stabilizing controllers, Fourier multipliers; - multivariable operator theory, model theory, commutant lifting theorems, coisometric realizations; - Hankel operators and forms; - operator algebras; - the Bellman function approach in singular integrals and harmonic analysis, singular integral operators and integral representations; - approximation in holomorphic spaces. These subjects are unified by the common "operator theoretic approach" and the systematic use of modern function theory techniques.
Download or read book Interpolation Schur Functions and Moment Problems written by Daniel Alpay and published by Springer Science & Business Media. This book was released on 2006-06-22 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: Schur analysis originated with an 1917 article which associated to a function, which is analytic and contractive in the open unit disk, a sequence, finite or infinite, of numbers in the open unit disk, called Schur coefficients, often named reflection coefficients in signal processing. This volume comprises seven essays dedicated to the analysis of Schur and Carathéodory functions and to the solutions of problems for these classes.
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 The Theory of H b Spaces 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: This is volume 1 of a 2 volume set.
