Convergence Problems Of Orthogonal Series
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Convergence Problems Of Orthogonal Series
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Author : G. Alexits
language : en
Publisher: Elsevier
Release Date : 2014-07-23
Convergence Problems Of Orthogonal Series written by G. Alexits and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-23 with Mathematics categories.
Convergence Problems of Orthogonal Series deals with the theory of convergence and summation of the general orthogonal series in relation to the general theory and classical expansions. The book reviews orthogonality, orthogonalization, series of orthogonal functions, complete orthogonal systems, and the Riesz-Fisher theorem. The text examines Jacobi polynomials, Haar's orthogonal system, and relations to the theory of probability using Rademacher's and Walsh's orthogonal systems. The book also investigates the convergence behavior of orthogonal series by methods belonging to the general theory of series. The text explains some Tauberian theorems and the classical Abel transform of the partial sums of a series which the investigator can use in the theory of orthogonal series. The book examines the importance of the Lebesgue functions for convergence problems, the generalization of the Walsh series, the order of magnitude of the Lebesgue functions, and the Lebesgue functions of the Cesaro summation. The text also deals with classical convergence problems in which general orthogonal series have limited significance as orthogonal expansions react upon the structural properties of the expanded function. This reaction happens under special assumptions concerning the orthogonal system in whose functions the expansion proceeds. The book can prove beneficial to mathematicians, students, or professor of calculus and advanced mathematics.
Convergence Problems Of Orthogonal Series
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Author : György Alexits
language : en
Publisher: Pergamon
Release Date : 1961
Convergence Problems Of Orthogonal Series written by György Alexits and has been published by Pergamon this book supported file pdf, txt, epub, kindle and other format this book has been release on 1961 with Convergence categories.
A Method Of Averaging In The Theory Of Orthogonal Series And Some Problems In The Theory Of Bases
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Author : Sergeĭ Viktorovich Bochkarev
language : en
Publisher: American Mathematical Soc.
Release Date : 1980
A Method Of Averaging In The Theory Of Orthogonal Series And Some Problems In The Theory Of Bases written by Sergeĭ Viktorovich Bochkarev 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 1980 with Mathematics categories.
"Investigate various forms of convergence of Fourier series in general orthonormal systems as well as certain problems in the theory of bases" -- Introduction.
Orthogonal Series
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Author : B. S. Kashin
language : en
Publisher: American Mathematical Soc.
Release Date : 2005-04-26
Orthogonal Series written by B. S. Kashin 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 2005-04-26 with Mathematics categories.
Introductory concepts and some general results Independent functions and their first applications The Haar system Some results on the trigonometric and Walsh systems The Hilbert transform and some function spaces The Faber-Schauder and Franklin systems Orthogonalization and factorization theorems Theorems on the convergence of general orthogonal series General theorems on the divergence of orthogonal series Some theorems on the representation of functions by orthogonal series
Mean Convergence On Orthogonal Series And Conjugate Series
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Author : Richard Askey
language : en
Publisher:
Release Date : 1961
Mean Convergence On Orthogonal Series And Conjugate Series written by Richard Askey and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1961 with Convergence categories.
Fourier Series And Orthogonal Polynomials
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Author : Dunham Jackson
language : en
Publisher: American Mathematical Soc.
Release Date : 1941-12-31
Fourier Series And Orthogonal Polynomials written by Dunham Jackson 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 1941-12-31 with Fourier series categories.
The underlying theme of this monograph is that the fundamental simplicity of the properties of orthogonal functions and the developments in series associated with them makes those functions important areas of study for students of both pure and applied mathematics. The book starts with Fourier series and goes on to Legendre polynomials and Bessel functions. Jackson considers a variety of boundary value problems using Fourier series and Laplace's equation. Chapter VI is an overview of Pearson frequency functions. Chapters on orthogonal, Jacobi, Hermite, and Laguerre functions follow. The final chapter deals with convergence. There is a set of exercises and a bibliography. For the reading of most of the book, no specific preparation is required beyond a first course in the calculus. A certain amount of “mathematical maturity” is presupposed or should be acquired in the course of the reading.
The Mean Convergence Of Orthogonal Series
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Author : George Milton Wing
language : en
Publisher:
Release Date : 1949
The Mean Convergence Of Orthogonal Series written by George Milton Wing and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1949 with Series, Orthogonal categories.
On Absolute Convergence Of Orthogonal Series I
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Author : S. B. Stechkin
language : en
Publisher:
Release Date : 1953
On Absolute Convergence Of Orthogonal Series I written by S. B. Stechkin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1953 with Trigonometrical functions categories.
Orthogonal Series
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Author : B. S. Kashin
language : en
Publisher:
Release Date : 1989
Orthogonal Series written by B. S. Kashin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Series, Orthogonal categories.
Fourier Series In Orthogonal Polynomials
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Author : Boris Osilenker
language : en
Publisher: World Scientific
Release Date : 1999-04-01
Fourier Series In Orthogonal Polynomials written by Boris Osilenker and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-04-01 with Mathematics categories.
This book presents a systematic course on general orthogonal polynomials and Fourier series in orthogonal polynomials. It consists of six chapters. Chapter 1 deals in essence with standard results from the university course on the function theory of a real variable and on functional analysis. Chapter 2 contains the classical results about the orthogonal polynomials (some properties, classical Jacobi polynomials and the criteria of boundedness). The main subject of the book is Fourier series in general orthogonal polynomials. Chapters 3 and 4 are devoted to some results in this topic (classical results about convergence and summability of Fourier series in L2μ; summability almost everywhere by the Cesaro means and the Poisson–Abel method for Fourier polynomial series are the subject of Chapters 4 and 5). The last chapter contains some estimates regarding the generalized shift operator and the generalized product formula, associated with general orthogonal polynomials. The starting point of the technique in Chapters 4 and 5 is the representations of bilinear and trilinear forms obtained by the author. The results obtained in these two chapters are new ones. Chapters 2 and 3 (and part of Chapter 1) will be useful to postgraduate students, and one can choose them for treatment. This book is intended for researchers (mathematicians, mechanicians and physicists) whose work involves function theory, functional analysis, harmonic analysis and approximation theory. Contents:Orthogonal Polynomials and Their PropertiesConvergence and Summability of Fourier Series in L2μFourier Orthogonal Series in Lrμ (1