Szegő S Theorem And Its Descendants

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Szegő's Theorem and Its Descendants

Barry Simon
Szeg s Theorem and Its Descendants Book PDF

Author : Barry Simon
Publisher : Princeton University Press
Page : 663 pages
File Size : 53,8 Mb
Release : 2010-11-08
Category : Mathematics
ISBN : 9781400837052

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Szegő's Theorem and Its Descendants by Barry Simon Pdf

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.

Spectral Analysis, Differential Equations and Mathematical Physics: A Festschrift in Honor of Fritz Gesztesy's 60th Birthday

Helge Holden,Barry Simon,Gerald Teschl
Spectral Analysis Differential Equations and Mathematical Physics A Festschrift in Honor of Fritz Gesztesy s 60th Birthday Book PDF

Author : Helge Holden,Barry Simon,Gerald Teschl
Publisher : American Mathematical Soc.
Page : 409 pages
File Size : 42,8 Mb
Release : 2013-07-08
Category : Mathematics
ISBN : 9780821875742

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Spectral Analysis, Differential Equations and Mathematical Physics: A Festschrift in Honor of Fritz Gesztesy's 60th Birthday by Helge Holden,Barry Simon,Gerald Teschl Pdf

This volume contains twenty contributions in the area of mathematical physics where Fritz Gesztesy made profound contributions. There are three survey papers in spectral theory, differential equations, and mathematical physics, which highlight, in particu

Convexity

Barry Simon
Convexity Book PDF

Author : Barry Simon
Publisher : Cambridge University Press
Page : 357 pages
File Size : 55,8 Mb
Release : 2011-05-19
Category : Mathematics
ISBN : 9781139497596

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Convexity by Barry Simon Pdf

Convexity is important in theoretical aspects of mathematics and also for economists and physicists. In this monograph the author provides a comprehensive insight into convex sets and functions including the infinite-dimensional case and emphasizing the analytic point of view. Chapter one introduces the reader to the basic definitions and ideas that play central roles throughout the book. The rest of the book is divided into four parts: convexity and topology on infinite-dimensional spaces; Loewner's theorem; extreme points of convex sets and related issues, including the Krein–Milman theorem and Choquet theory; and a discussion of convexity and inequalities. The connections between disparate topics are clearly explained, giving the reader a thorough understanding of how convexity is useful as an analytic tool. A final chapter overviews the subject's history and explores further some of the themes mentioned earlier. This is an excellent resource for anyone interested in this central topic.

The Moment Problem

Konrad Schmüdgen
The Moment Problem Book PDF

Author : Konrad Schmüdgen
Publisher : Springer
Page : 512 pages
File Size : 54,5 Mb
Release : 2017-11-09
Category : Mathematics
ISBN : 9783319645469

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The Moment Problem by Konrad Schmüdgen Pdf

This advanced textbook provides a comprehensive and unified account of the moment problem. It covers the classical one-dimensional theory and its multidimensional generalization, including modern methods and recent developments. In both the one-dimensional and multidimensional cases, the full and truncated moment problems are carefully treated separately. Fundamental concepts, results and methods are developed in detail and accompanied by numerous examples and exercises. Particular attention is given to powerful modern techniques such as real algebraic geometry and Hilbert space operators. A wide range of important aspects are covered, including the Nevanlinna parametrization for indeterminate moment problems, canonical and principal measures for truncated moment problems, the interplay between Positivstellensätze and moment problems on semi-algebraic sets, the fibre theorem, multidimensional determinacy theory, operator-theoretic approaches, and the existence theory and important special topics of multidimensional truncated moment problems. The Moment Problem will be particularly useful to graduate students and researchers working on moment problems, functional analysis, complex analysis, harmonic analysis, real algebraic geometry, polynomial optimization, or systems theory. With notes providing useful background information and exercises of varying difficulty illustrating the theory, this book will also serve as a reference on the subject and can be used for self-study.

Invariant Random Fields on Spaces with a Group Action

Anatoliy Malyarenko
Invariant Random Fields on Spaces with a Group Action Book PDF

Author : Anatoliy Malyarenko
Publisher : Springer Science & Business Media
Page : 271 pages
File Size : 42,8 Mb
Release : 2012-10-26
Category : Mathematics
ISBN : 9783642334061

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Invariant Random Fields on Spaces with a Group Action by Anatoliy Malyarenko Pdf

The author describes the current state of the art in the theory of invariant random fields. This theory is based on several different areas of mathematics, including probability theory, differential geometry, harmonic analysis, and special functions. The present volume unifies many results scattered throughout the mathematical, physical, and engineering literature, as well as it introduces new results from this area first proved by the author. The book also presents many practical applications, in particular in such highly interesting areas as approximation theory, cosmology and earthquake engineering. It is intended for researchers and specialists working in the fields of stochastic processes, statistics, functional analysis, astronomy, and engineering.

Operator Methods in Mathematical Physics

Jan Janas,Pavel Kurasov,A. Laptev,Sergei Naboko
Operator Methods in Mathematical Physics Book PDF

Author : Jan Janas,Pavel Kurasov,A. Laptev,Sergei Naboko
Publisher : Springer Science & Business Media
Page : 184 pages
File Size : 53,9 Mb
Release : 2013-01-08
Category : Mathematics
ISBN : 9783034805315

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Operator Methods in Mathematical Physics by Jan Janas,Pavel Kurasov,A. Laptev,Sergei Naboko Pdf

The conference Operator Theory, Analysis and Mathematical Physics – OTAMP is a regular biennial event devoted to mathematical problems on the border between analysis and mathematical physics. The current volume presents articles written by participants, mostly invited speakers, and is devoted to problems at the forefront of modern mathematical physics such as spectral properties of CMV matrices and inverse problems for the non-classical Schrödinger equation. Other contributions deal with equations from mathematical physics and study their properties using methods of spectral analysis. The volume explores several new directions of research and may serve as a source of new ideas and problems for all scientists interested in modern mathematical physics.

Topics in Clifford Analysis

Swanhild Bernstein
Topics in Clifford Analysis Book PDF

Author : Swanhild Bernstein
Publisher : Springer Nature
Page : 503 pages
File Size : 52,5 Mb
Release : 2019-10-15
Category : Mathematics
ISBN : 9783030238544

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Topics in Clifford Analysis by Swanhild Bernstein Pdf

Quaternionic and Clifford analysis are an extension of complex analysis into higher dimensions. The unique starting point of Wolfgang Sprößig’s work was the application of quaternionic analysis to elliptic differential equations and boundary value problems. Over the years, Clifford analysis has become a broad-based theory with a variety of applications both inside and outside of mathematics, such as higher-dimensional function theory, algebraic structures, generalized polynomials, applications of elliptic boundary value problems, wavelets, image processing, numerical and discrete analysis. The aim of this volume is to provide an essential overview of modern topics in Clifford analysis, presented by specialists in the field, and to honor the valued contributions to Clifford analysis made by Wolfgang Sprößig throughout his career.

Approximation Theory XV: San Antonio 2016

Gregory E. Fasshauer,Larry L. Schumaker
Approximation Theory XV San Antonio 2016 Book PDF

Author : Gregory E. Fasshauer,Larry L. Schumaker
Publisher : Springer
Page : 398 pages
File Size : 53,5 Mb
Release : 2017-07-19
Category : Mathematics
ISBN : 9783319599120

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Approximation Theory XV: San Antonio 2016 by Gregory E. Fasshauer,Larry L. Schumaker Pdf

These proceedings are based on papers presented at the international conference Approximation Theory XV, which was held May 22–25, 2016 in San Antonio, Texas. The conference was the fifteenth in a series of meetings in Approximation Theory held at various locations in the United States, and was attended by 146 participants. The book contains longer survey papers by some of the invited speakers covering topics such as compressive sensing, isogeometric analysis, and scaling limits of polynomials and entire functions of exponential type. The book also includes papers on a variety of current topics in Approximation Theory drawn from areas such as advances in kernel approximation with applications, approximation theory and algebraic geometry, multivariate splines for applications, practical function approximation, approximation of PDEs, wavelets and framelets with applications, approximation theory in signal processing, compressive sensing, rational interpolation, spline approximation in isogeometric analysis, approximation of fractional differential equations, numerical integration formulas, and trigonometric polynomial approximation.

Recent Advances in Orthogonal Polynomials, Special Functions, and Their Applications

Jorge Arvesœ,Guillermo Lopez Lagomasino
Recent Advances in Orthogonal Polynomials Special Functions and Their Applications Book PDF

Author : Jorge Arvesœ,Guillermo Lopez Lagomasino
Publisher : American Mathematical Soc.
Page : 266 pages
File Size : 45,9 Mb
Release : 2012-09-11
Category : Mathematics
ISBN : 9780821868966

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Recent Advances in Orthogonal Polynomials, Special Functions, and Their Applications by Jorge Arvesœ,Guillermo Lopez Lagomasino Pdf

This volume contains the proceedings of the 11th International Symposium on Orthogonal Polynomials, Special Functions, and their Applications, held August 29-September 2, 2011, at the Universidad Carlos III de Madrid in Leganes, Spain. The papers cover asymptotic properties of polynomials on curves of the complex plane, universality behavior of sequences of orthogonal polynomials for large classes of measures and its application in random matrix theory, the Riemann-Hilbert approach in the study of Pade approximation and asymptotics of orthogonal polynomials, quantum walks and CMV matrices, spectral modifications of linear functionals and their effect on the associated orthogonal polynomials, bivariate orthogonal polynomials, and optimal Riesz and logarithmic energy distribution of points. The methods used include potential theory, boundary values of analytic functions, Riemann-Hilbert analysis, and the steepest descent method.

Geometric Science of Information

Frank Nielsen,Frédéric Barbaresco
Geometric Science of Information Book PDF

Author : Frank Nielsen,Frédéric Barbaresco
Publisher : Springer
Page : 764 pages
File Size : 40,5 Mb
Release : 2019-08-19
Category : Computers
ISBN : 9783030269807

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Geometric Science of Information by Frank Nielsen,Frédéric Barbaresco Pdf

This book constitutes the proceedings of the 4th International Conference on Geometric Science of Information, GSI 2019, held in Toulouse, France, in August 2019. The 79 full papers presented in this volume were carefully reviewed and selected from 105 submissions. They cover all the main topics and highlights in the domain of geometric science of information, including information geometry manifolds of structured data/information and their advanced applications.

Orthogonal Polynomials on the Unit Circle

Barry Simon
Orthogonal Polynomials on the Unit Circle Book PDF

Author : Barry Simon
Publisher : American Mathematical Soc.
Page : 498 pages
File Size : 54,5 Mb
Release : 2009-08-05
Category : Mathematics
ISBN : 9780821848630

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Orthogonal Polynomials on the Unit Circle by Barry Simon Pdf

This two-part book is 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 Schrodinger operators. Among the topics discussed along the way are the asymptotics of Toeplitz determinants (Szego's theorems), limit theorems for the density of the zeros of orthogonal polynomials, matrix representations for multiplication by $z$ (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.

Analytic Combinatorics in Several Variables

Robin Pemantle,Mark C. Wilson
Analytic Combinatorics in Several Variables Book PDF

Author : Robin Pemantle,Mark C. Wilson
Publisher : Cambridge University Press
Page : 395 pages
File Size : 55,9 Mb
Release : 2013-05-31
Category : Mathematics
ISBN : 9781107031579

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Analytic Combinatorics in Several Variables by Robin Pemantle,Mark C. Wilson Pdf

Aimed at graduate students and researchers in enumerative combinatorics, this book is the first to treat the analytic aspects of combinatorial enumeration from a multivariate perspective.

Schrödinger Operators

Hans L. Cycon,Barry Simon
Schr dinger Operators Book PDF

Author : Hans L. Cycon,Barry Simon
Publisher : Springer Science & Business Media
Page : 337 pages
File Size : 46,5 Mb
Release : 1987
Category : Computers
ISBN : 9783540167587

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Schrödinger Operators by Hans L. Cycon,Barry Simon Pdf

Are you looking for a concise summary of the theory of Schrödinger operators? Here it is. Emphasizing the progress made in the last decade by Lieb, Enss, Witten and others, the three authors don’t just cover general properties, but also detail multiparticle quantum mechanics – including bound states of Coulomb systems and scattering theory. This corrected and extended reprint contains updated references as well as notes on the development in the field over the past twenty years.

Discrete and Continuous Boundary Problems

Atkinson
Discrete and Continuous Boundary Problems Book PDF

Author : Atkinson
Publisher : Academic Press
Page : 586 pages
File Size : 45,6 Mb
Release : 1964-01-01
Category : Computers
ISBN : 9780080955162

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Discrete and Continuous Boundary Problems by Atkinson Pdf

Discrete and Continuous Boundary Problems

Orthogonal Polynomials

Gabor Szegš
Orthogonal Polynomials Book PDF

Author : Gabor Szegš
Publisher : American Mathematical Soc.
Page : 448 pages
File Size : 46,8 Mb
Release : 1939-12-31
Category : Mathematics
ISBN : 9780821810231

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Orthogonal Polynomials by Gabor Szegš Pdf

The general theory of orthogonal polynomials was developed in the late 19th century from a study of continued fractions by P. L. Chebyshev, even though special cases were introduced earlier by Legendre, Hermite, Jacobi, Laguerre, and Chebyshev himself. It was further developed by A. A. Markov, T. J. Stieltjes, and many other mathematicians. The book by Szego, originally published in 1939, is the first monograph devoted to the theory of orthogonal polynomials and its applications in many areas, including analysis, differential equations, probability and mathematical physics. Even after all the years that have passed since the book first appeared, and with many other books on the subject published since then, this classic monograph by Szego remains an indispensable resource both as a textbook and as a reference book. It can be recommended to anyone who wants to be acquainted with this central topic of mathematical analysis.