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The Classical Moment Problem And Some Related Questions In Analysis By Ni Akhiezer
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Book Synopsis The Classical Moment Problem by : N. I. Akhiezer
Download or read book The Classical Moment Problem written by N. I. Akhiezer and published by Courier Dover Publications. This book was released on 2020-12-16 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text provides a classic treatment of issues associated with the moment problem that also involve linear algebra, probability theory, stochastic processes, quantum fields, signal processing, and more. 1965 edition.
Book Synopsis The Classical Moment Problem and Some Related Questions in Analysis by : N.I. Akhiezer
Download or read book The Classical Moment Problem and Some Related Questions in Analysis written by N.I. Akhiezer and published by SIAM. This book was released on 2020-12-01 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: The mathematical theory for many application areas depends on a deep understanding of the theory of moments. These areas include medical imaging, signal processing, computer visualization, and data science. The problem of moments has also found novel applications to areas such as control theory, image analysis, signal processing, polynomial optimization, and statistical big data. The Classical Moment Problem and Some Related Questions in Analysis presents a unified treatment of the development of the classical moment problem from the late 19th century to the middle of the 20th century. Important connections between the moment problem and many branches of analysis are presented. In this self-contained text, readers will find a unified exposition of important classical results, which are difficult to read in the original journals, as well as a strong foundation for many areas in modern applied mathematics. Researchers in areas that use techniques developed for the classical moment problem will find the book of interest.
Book Synopsis The Classical Moment Problem by : Naum Ilʹich Akhiezer
Download or read book The Classical Moment Problem written by Naum Ilʹich Akhiezer and published by . This book was released on 1965 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Classical Moment Problem and Some Related Questions in Analysis [by] N.I. Akhiezer by : Naum Ilʹich Akhiezer
Download or read book The Classical Moment Problem and Some Related Questions in Analysis [by] N.I. Akhiezer written by Naum Ilʹich Akhiezer and published by . This book was released on 1965 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The classical moment problem and some related questions in analysis, tr by : Naum Ilʹich Akhiezer
Download or read book The classical moment problem and some related questions in analysis, tr written by Naum Ilʹich Akhiezer and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Classical Moment Problem and Some Related Questions in Analysis. Translated by N. Kemmer by : Naum Ilʹich Akhiezer
Download or read book The Classical Moment Problem and Some Related Questions in Analysis. Translated by N. Kemmer written by Naum Ilʹich Akhiezer and published by . This book was released on 1965 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Featured Reviews in Mathematical Reviews 1997-1999 by : Donald G. Babbitt
Download or read book Featured Reviews in Mathematical Reviews 1997-1999 written by Donald G. Babbitt and published by American Mathematical Soc.. This book was released on 2000-05-05 with total page 762 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second volume of Featured Reviews makes available special detailed reviews of some of the most important mathematical articles and books published from 1997 through 1999. Also included are excellent reviews of several classic books and articles published prior to 1970. Among those reviews, for example, are the following: Homological Algebra by Henri Cartan and Samuel Eilenberg, reviewed by G. Hochschild; Faisceaux algebriques coherents by Jean-Pierre Serre, reviewed by C. Chevalley; and On the Theory of General Partial Differential Operators by Lars Hormander, reviewed by J. L. Lions. In particular, those seeking information on current developments outside their own area of expertise will find the volume very useful. By identifying some of the best publications, papers, and books that have had or are expected to have a significant impact in applied and pure mathematics, this volume will serve as a comprehensive guide to important new research across all fields covered by MR.
Book Synopsis Operator Theory and Related Topics by : V.M. Adamyan
Download or read book Operator Theory and Related Topics written by V.M. Adamyan and published by Springer Science & Business Media. This book was released on 2000-03-01 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present book is the second of the two volume Proceedings of the Mark Krein International Conference on Operator Theory and Applications. This conference, which was dedicated to the 90th Anniversary of the prominent mathematician Mark Krein, was held in Odessa, Ukraine from 18-22 August, 1997. The conference focused on the main ideas, methods, results, and achievements of M. G. Krein. This second volume is devoted to operator theory and related topics. It opens with the bibliography of M. G. Krein and a number of survey papers about his work. The main part of the book consists of original research papers presenting the state of the art in operator theory and its applications. The first volume of these proceedings, entitled Differential Operators and related Topics, concerns the other aspects of the conference. The two volumes will be of interest to a wide-range of readership in pure and applied mathematics, physics and engineering sciences. Table of Contents Preface. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii Bibliography of Mark Grigorevich Krein . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix Review papers: M. G. Krein's Contributions to Prediction Theory H. Dym M. G. Krein's Contribution to the Moment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 AA Nudelman Research Papers: Solution of the Truncated Matrix Hamburger Moment Problem according to M. G. Krein . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 Y. M. Adamyan and I. M. Tkachenko Extreme Points of a Positive Operator Ball . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 T. Ando M-accretive Extensions of Sectorial Operators and Krein Spaces . . . . . . . . . 67 Y. M. Arlinskii A Simple Proof of the Continuous Commutant Lifting Theorem . . . . . . . . . . 83 R. Bruzual and M.
Book Synopsis Recent Progress in Functional Analysis by : K.D. Bierstedt
Download or read book Recent Progress in Functional Analysis written by K.D. Bierstedt and published by Elsevier. This book was released on 2001-09-20 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Proceedings Volume contains 32 articles on various interesting areas ofpresent-day functional analysis and its applications: Banach spaces andtheir geometry, operator ideals, Banach and operator algebras, operator andspectral theory, Frechet spaces and algebras, function and sequence spaces.The authors have taken much care with their articles and many papers presentimportant results and methods in active fields of research. Several surveytype articles (at the beginning and the end of the book) will be very usefulfor mathematicians who want to learn "what is going on" in some particularfield of research.
Book Synopsis Orthogonal Polynomials on the Unit Circle: Spectral theory by : Barry Simon
Download or read book Orthogonal Polynomials on the Unit Circle: Spectral theory written by Barry Simon and published by American Mathematical Soc.. This book was released on 2005 with total page 608 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents an overview of the theory of probability measures on the unit circle, viewed especially in terms of the orthogonal polynomials defined by those measures. This book discusses topics such as asymptotics of Toeplitz determinants (Szego's theorems), and limit theorems for the density of the zeros of orthogonal polynomials.
Book Synopsis Orthogonal Polynomials on the Unit Circle by : Barry Simon
Download or read book Orthogonal Polynomials on the Unit Circle written by Barry Simon and published by American Mathematical Soc.. This book was released on 2005 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two-part volume gives a comprehensive overview of the theory of probability measures on the unit circle, viewed especially in terms of the orthogonal polynomials defined by those measures. A major theme involves the connections between the Verblunsky coefficients (the coefficients of the recurrence equation for the orthogonal polynomials) and the measures, an analog of the spectral theory of one-dimensional Schrödinger operators. Among the topics discussed along the way are the asymptotics of Toeplitz determinants (Szegő's theorems), limit theorems for the density of the zeros of orthogonal polynomials, matrix representations for multiplication by (CMV matrices), periodic Verblunsky coefficients from the point of view of meromorphic functions on hyperelliptic surfaces, and connections between the theories of orthogonal polynomials on the unit circle and on the real line. The book is suitable for graduate students and researchers interested in analysis.
Book Synopsis Problems and Recent Methods in Operator Theory by : Fernanda Botelho
Download or read book Problems and Recent Methods in Operator Theory written by Fernanda Botelho and published by American Mathematical Soc.. This book was released on 2017-04-18 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the Workshop on Problems and Recent Methods in Operator Theory, held at the University of Memphis, Memphis, TN, from October 15–16, 2015 and the AMS Special Session on Advances in Operator Theory and Applications, in Memory of James Jamison, held at the University of Memphis, Memphis, TN, from October 17–18, 2015. Operator theory is at the root of several branches of mathematics and offers a broad range of challenging and interesting research problems. It also provides powerful tools for the development of other areas of science including quantum theory, physics and mechanics. Isometries have applications in solid-state physics. Hermitian operators play an integral role in quantum mechanics very much due to their “nice” spectral properties. These powerful connections demonstrate the impact of operator theory in various branches of science. The articles in this volume address recent problems and research advances in operator theory. Highlighted topics include spectral, structural and geometric properties of special types of operators on Banach spaces, with emphasis on isometries, weighted composition operators, multi-circular projections on function spaces, as well as vector valued function spaces and spaces of analytic functions. This volume gives a succinct overview of state-of-the-art techniques from operator theory as well as applications to classical problems and long-standing open questions.
Book Synopsis Inverse Linear Problems on Hilbert Space and their Krylov Solvability by : Noè Angelo Caruso
Download or read book Inverse Linear Problems on Hilbert Space and their Krylov Solvability written by Noè Angelo Caruso and published by Springer Nature. This book was released on 2022-02-10 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a thorough discussion of the theory of abstract inverse linear problems on Hilbert space. Given an unknown vector f in a Hilbert space H, a linear operator A acting on H, and a vector g in H satisfying Af=g, one is interested in approximating f by finite linear combinations of g, Ag, A2g, A3g, ... The closed subspace generated by the latter vectors is called the Krylov subspace of H generated by g and A. The possibility of solving this inverse problem by means of projection methods on the Krylov subspace is the main focus of this text. After giving a broad introduction to the subject, examples and counterexamples of Krylov-solvable and non-solvable inverse problems are provided, together with results on uniqueness of solutions, classes of operators inducing Krylov-solvable inverse problems, and the behaviour of Krylov subspaces under small perturbations. An appendix collects material on weaker convergence phenomena in general projection methods. This subject of this book lies at the boundary of functional analysis/operator theory and numerical analysis/approximation theory and will be of interest to graduate students and researchers in any of these fields.
Book Synopsis Lectures on Integral Transforms by : Naum Il_ich Akhiezer
Download or read book Lectures on Integral Transforms written by Naum Il_ich Akhiezer and published by American Mathematical Soc.. This book was released on 1988-12-31 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focuses on classical integral transforms, principally the Fourier transform, and their applications. This book develops the general theory of the Fourier transform for the space $L DEGREES1(E_n)$ of integrable functions of $n$ var
Book Synopsis Operator Theory and Indefinite Inner Product Spaces by : Matthias Langer
Download or read book Operator Theory and Indefinite Inner Product Spaces written by Matthias Langer and published by Springer Science & Business Media. This book was released on 2006-06-16 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: A colloquium on operator theory was held in Vienna, Austria, in March 2004, on the occasion of the retirement of Heinz Langer, a leading expert in operator theory and indefinite inner product spaces. The book contains fifteen refereed articles reporting on recent and original results in various areas of operator theory, all of them related with the work of Heinz Langer. The topics range from abstract spectral theory in Krein spaces to more concrete applications, such as boundary value problems, the study of orthogonal functions, or moment problems. The book closes with a historical survey paper.
Book Synopsis Inverse Problems and Nonlinear Evolution Equations by : Alexander L. Sakhnovich
Download or read book Inverse Problems and Nonlinear Evolution Equations written by Alexander L. Sakhnovich and published by Walter de Gruyter. This book was released on 2013-07-31 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on the method of operator identities and related theory of S-nodes, both developed by Lev Sakhnovich. The notion of the transfer matrix function generated by the S-node plays an essential role. The authors present fundamental solutions of various important systems of differential equations using the transfer matrix function, that is, either directly in the form of the transfer matrix function or via the representation in this form of the corresponding Darboux matrix, when Bäcklund–Darboux transformations and explicit solutions are considered. The transfer matrix function representation of the fundamental solution yields solution of an inverse problem, namely, the problem to recover system from its Weyl function. Weyl theories of selfadjoint and skew-selfadjoint Dirac systems, related canonical systems, discrete Dirac systems, system auxiliary to the N-wave equation and a system rationally depending on the spectral parameter are obtained in this way. The results on direct and inverse problems are applied in turn to the study of the initial-boundary value problems for integrable (nonlinear) wave equations via inverse spectral transformation method. Evolution of the Weyl function and solution of the initial-boundary value problem in a semi-strip are derived for many important nonlinear equations. Some uniqueness and global existence results are also proved in detail using evolution formulas. The reading of the book requires only some basic knowledge of linear algebra, calculus and operator theory from the standard university courses.
Book Synopsis Szegő's Theorem and Its Descendants by : Barry Simon
Download or read book Szegő's Theorem and Its Descendants written by Barry Simon and published by Princeton University Press. This book was released on 2010-11-08 with total page 663 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a comprehensive overview of the sum rule approach to spectral analysis of orthogonal polynomials, which derives from Gábor Szego's classic 1915 theorem and its 1920 extension. Barry Simon emphasizes necessary and sufficient conditions, and provides mathematical background that until now has been available only in journals. Topics include background from the theory of meromorphic functions on hyperelliptic surfaces and the study of covering maps of the Riemann sphere with a finite number of slits removed. This allows for the first book-length treatment of orthogonal polynomials for measures supported on a finite number of intervals on the real line. In addition to the Szego and Killip-Simon theorems for orthogonal polynomials on the unit circle (OPUC) and orthogonal polynomials on the real line (OPRL), Simon covers Toda lattices, the moment problem, and Jacobi operators on the Bethe lattice. Recent work on applications of universality of the CD kernel to obtain detailed asymptotics on the fine structure of the zeros is also included. The book places special emphasis on OPRL, which makes it the essential companion volume to the author's earlier books on OPUC.
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