The Classical Moment Problem
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The Classical Moment Problem
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Author : N. I. Akhiezer
language : en
Publisher: Courier Dover Publications
Release Date : 2020-12-16
The Classical Moment Problem written by N. I. Akhiezer and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-16 with Mathematics categories.
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.
The Classical Moment Problem
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Author : Naum Ilʹich Akhiezer
language : en
Publisher:
Release Date : 1965
The Classical Moment Problem written by Naum Ilʹich Akhiezer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1965 with Functional analysis categories.
The Classical Moment Problem And Some Related Questions In Analysis
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Author : N.I. Akhiezer
language : en
Publisher: SIAM
Release Date : 2020-12-01
The Classical Moment Problem And Some Related Questions In Analysis written by N.I. Akhiezer and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-01 with Mathematics categories.
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.
The Classical Moment Problem
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Author : Naum Ilʹich Akhiezer
language : en
Publisher:
Release Date : 1965
The Classical Moment Problem written by Naum Ilʹich Akhiezer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1965 with Theory of distributions (Functional analysis) categories.
The Classical Moment Problem And Some Related Questions In Analysis
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Author : Naum Ilʹich Akhiezer
language : en
Publisher:
Release Date : 1977
The Classical Moment Problem And Some Related Questions In Analysis written by Naum Ilʹich Akhiezer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1977 with categories.
The Problem Of Moments
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Author : James Alexander Shohat
language : en
Publisher: American Mathematical Soc.
Release Date : 1943-12-31
The Problem Of Moments written by James Alexander Shohat 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 1943-12-31 with Mathematics categories.
The book was first published in 1943 and then was reprinted several times with corrections. It presents the development of the classical problem of moments for the first 50 years, after its introduction by Stieltjes in the 1890s. In addition to initial developments by Stieltjes, Markov, and Chebyshev, later contributions by Hamburger, Nevanlinna, Hausdorff, Stone, and others are discussed. The book also contains some results on the trigonometric moment problem and a chapter devoted to approximate quadrature formulas.
The Problem Of Moments
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Author : James Alexander Shohat
language : en
Publisher: American Mathematical Society(RI)
Release Date : 1950
The Problem Of Moments written by James Alexander Shohat and has been published by American Mathematical Society(RI) this book supported file pdf, txt, epub, kindle and other format this book has been release on 1950 with Mathematics categories.
Presents the development of the classical problem of moments for the first 50 years, after its introduction by Stieltjes in the 1890s. This book discusses the initial developments by Stieltjes, Markov, and Chebyshev, and later contributions by Hamburger, Nevanlinna, Hausdorff, and Stone.
The Classical Moment Problem And Some Related Questions In Analysis Tr
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Author : Naum Ilʹich Akhiezer
language : en
Publisher:
Release Date :
The Classical Moment Problem And Some Related Questions In Analysis Tr written by Naum Ilʹich Akhiezer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with Moment spaces categories.
The Moment Problem
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Author : Konrad Schmüdgen
language : en
Publisher: Springer
Release Date : 2017-11-09
The Moment Problem written by Konrad Schmüdgen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-09 with Mathematics categories.
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.
Moments In Mathematics
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Author : Henry J. Landau
language : en
Publisher: American Mathematical Soc.
Release Date : 1987
Moments In Mathematics written by Henry J. Landau 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 1987 with Inequalities categories.
Function theory, spectral decomposition of operators, probability, approximation, electrical and mechanical inverse problems, prediction of stochastic processes, the design of algorithms for signal-processing VLSI chips--these are among a host of important theoretical and applied topics illuminated by the classical moment problem. To survey some of these ramifications and the research which derives from them, the AMS sponsored the Short Course Moments in Mathematics at the Joint Mathematics Meetings, held in San Antonio, Texas, in January 1987. This volume contains the six lectures presented during that course. The papers are likely to find a wide audience, for they are expository, but nevertheless lead the reader to topics of current research. In his paper, Henry J. Landau sketches the main ideas of past work related to the moment problem by such mathematicians as Caratheodory, Herglotz, Schur, Riesz, and Krein and describes the way the moment problem has interconnected so many diverse areas of research. J. H. B. Kemperman examines the moment problem from a geometric viewpoint which involves a certain natural duality method and leads to interesting applications in linear programming, measure theory, and dilations. Donald Sarason first provides a brief review of the theory of unbounded self-adjoint operators then goes on to sketch the operator-theoretic treatment of the Hamburger problem and to discuss Hankel operators, the Adamjan-Arov-Krein approach, and the theory of unitary dilations. Exploring the interplay of trigonometric moment problems and signal processing, Thomas Kailath describes the role of Szego polynomials in linear predictive coding methods, parallel implementation, one-dimensional inverse scattering problems, and the Toeplitz moment matrices. Christian Berg contrasts the multi-dimensional moment problem with the one-dimensional theory and shows how the theory of the moment problem may be viewed as part of harmonic analysis on semigroups. Starting from a historical survey of the use of moments in probability and statistics, Persi Diaconis illustrates the continuing vitality of these methods in a variety of recent novel problems drawn from such areas as Wiener-Ito integrals, random graphs and matrices, Gibbs ensembles, cumulants and self-similar processes, projections of high-dimensional data, and empirical estimation.
