Jacobi Matrices And The Moment Problem

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Jacobi Matrices And The Moment Problem

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Author : Yurij M. Berezansky
language : en
Publisher: Springer Nature
Release Date : 2023-11-29

Jacobi Matrices And The Moment Problem written by Yurij M. Berezansky and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-11-29 with Mathematics categories.

This monograph presents the solution of the classical moment problem, the construction of Jacobi matrices and corresponding polynomials. The cases of strongly,trigonometric, complex and real two-dimensional moment problems are discussed, and the Jacobi-type matrices corresponding to the trigonometric moment problem are shown. The Berezansky theory of the expansion in generalized eigenvectors for corresponding set of commuting operators plays the key role in the proof of results. The book is recommended for researchers in fields of functional analysis, operator theory, mathematical physics, and engineers who deal with problems of coupled pendulums.

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.

Some Questions In The Theory Of Moments

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Author : Mark Grigorʹevich Kreĭn
language : en
Publisher: American Mathematical Soc.
Release Date : 1968

Some Questions In The Theory Of Moments written by Mark Grigorʹevich Kreĭn 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 1968 with Functional analysis 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.

Laredo Lectures On Orthogonal Polynomials And Special Functions

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Author : Renato Alvarez-Nodarse
language : en
Publisher: Nova Publishers
Release Date : 2004

Laredo Lectures On Orthogonal Polynomials And Special Functions written by Renato Alvarez-Nodarse and has been published by Nova Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.

This new book presents research in orthogonal polynomials and special functions. Recent developments in the theory and accomplishments of the last decade are pointed out and directions for research in the future are identified. The topics covered include matrix orthogonal polynomials, spectral theory and special functions, Asymptotics for orthogonal polynomials via Riemann-Hilbert methods, Polynomial wavelets and Koornwinder polynomials.

Iterated Function Systems Moments And Transformations Of Infinite Matrices

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Author : Palle E. T. Jørgensen
language : en
Publisher: American Mathematical Soc.
Release Date : 2011

Iterated Function Systems Moments And Transformations Of Infinite Matrices written by Palle E. T. Jørgensen 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 2011 with Mathematics categories.

The authors study the moments of equilibrium measures for iterated function systems (IFSs) and draw connections to operator theory. Their main object of study is the infinite matrix which encodes all the moment data of a Borel measure on $\mathbb{R}^d$ or $\mathbb{C}$. To encode the salient features of a given IFS into precise moment data, they establish an interdependence between IFS equilibrium measures, the encoding of the sequence of moments of these measures into operators, and a new correspondence between the IFS moments and this family of operators in Hilbert space. For a given IFS, the authors' aim is to establish a functorial correspondence in such a way that the geometric transformations of the IFS turn into transformations of moment matrices, or rather transformations of the operators that are associated with them.

The Problem Of Moments

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Author : James Shohat
language : en
Publisher: American Mathematical Society(RI)
Release Date : 1950

The Problem Of Moments written by James 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.

Modern Analysis And Applications

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Author : Vadim Adamyan
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-08-29

Modern Analysis And Applications written by Vadim Adamyan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-08-29 with Mathematics categories.

This is the second of two volumes containing peer-reviewed research and survey papers based on talks at the International Conference on Modern Analysis and Applications. The papers describe the contemporary development of subjects influenced by Mark Krein.

Matrices Moments And Quadrature With Applications

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Author : Gene H. Golub
language : en
Publisher: Princeton University Press
Release Date : 2009-12-07

Matrices Moments And Quadrature With Applications written by Gene H. Golub and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-12-07 with Mathematics categories.

This computationally oriented book describes and explains the mathematical relationships among matrices, moments, orthogonal polynomials, quadrature rules, and the Lanczos and conjugate gradient algorithms. The book bridges different mathematical areas to obtain algorithms to estimate bilinear forms involving two vectors and a function of the matrix. The first part of the book provides the necessary mathematical background and explains the theory. The second part describes the applications and gives numerical examples of the algorithms and techniques developed in the first part. Applications addressed in the book include computing elements of functions of matrices; obtaining estimates of the error norm in iterative methods for solving linear systems and computing parameters in least squares and total least squares; and solving ill-posed problems using Tikhonov regularization. This book will interest researchers in numerical linear algebra and matrix computations, as well as scientists and engineers working on problems involving computation of bilinear forms.

Approximation Methods And Analytical Modeling Using Partial Differential Equations

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Author : Tamara Fastovska
language : en
Publisher: Frontiers Media SA
Release Date : 2025-03-28

Approximation Methods And Analytical Modeling Using Partial Differential Equations written by Tamara Fastovska and has been published by Frontiers Media SA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-28 with Science categories.

Adequate mathematical modeling is the key to success for many real-world projects in engineering, medicine, and other applied areas. As soon as an appropriate mathematical model is developed, it can be comprehensively analyzed by a broad spectrum of available mathematical methods. For example, compartmental models are widely used in mathematical epidemiology to describe the dynamics of infectious diseases and in mathematical models of population genetics. While the existence of an optimal solution under certain condition can be often proved rigorously, this does not always mean that such a solution is easy to implement in practice. Finding a reasonable approximation can in itself be a challenging research problem. This Research Topic is devoted to modeling, analysis, and approximation problems whose solutions exploit and explore the theory of partial differential equations. It aims to highlight new analytical tools for use in the modeling of problems arising in applied sciences and practical areas. Researchers are invited to submit articles that investigate the qualitative behavior of weak solutions (removability conditions for singularities), the dependence of the local asymptotic property of these solutions on initial and boundary data, and also the existence of solutions. Contributors are particularly encouraged to focus on anisotropic models: analyzing the preconditions on the strength of the anisotropy, and comparing the analytical estimates for the growth behavior of the solutions near the singularities with the observed growth in numerical simulations. The qualitative analysis and analytical results should be confirmed by the numerically observed solution behavior.