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Convergence Problems Of Orthogonal Series
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Book Synopsis Convergence Problems of Orthogonal Series by : G. Alexits
Download or read book Convergence Problems of Orthogonal Series written by G. Alexits and published by Elsevier. This book was released on 2014-07-23 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Convergence Problems of Orthogonal Series by : György Alexits
Download or read book Convergence Problems of Orthogonal Series written by György Alexits and published by Pergamon. This book was released on 1961 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Convergence problems of orthogonal series by : György Alexits
Download or read book Convergence problems of orthogonal series written by György Alexits and published by . This book was released on 1961 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Convergence Problems of Orthogonal Series by : George Alexits
Download or read book Convergence Problems of Orthogonal Series written by George Alexits and published by . This book was released on 1961 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Method of Averaging in the Theory of Orthogonal Series and Some Problems in the Theory of Bases by : Sergeĭ Viktorovich Bochkarev
Download or read book A Method of Averaging in the Theory of Orthogonal Series and Some Problems in the Theory of Bases written by Sergeĭ Viktorovich Bochkarev and published by American Mathematical Soc.. This book was released on 1980 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Investigate various forms of convergence of Fourier series in general orthonormal systems as well as certain problems in the theory of bases" -- Introduction.
Book Synopsis Konvergenzprobleme der Orthogonalreihen. Convergence Problems of Orthogonal Series. (Translated by I. Földes.). by : György ALEXITS
Download or read book Konvergenzprobleme der Orthogonalreihen. Convergence Problems of Orthogonal Series. (Translated by I. Földes.). written by György ALEXITS and published by . This book was released on 1961 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Mean Convergence on Orthogonal Series and Conjugate Series by : Richard Askey
Download or read book Mean Convergence on Orthogonal Series and Conjugate Series written by Richard Askey and published by . This book was released on 1961 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Mean Convergence of Orthogonal Series by : George Milton Wing
Download or read book The Mean Convergence of Orthogonal Series written by George Milton Wing and published by . This book was released on 1949 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Fourier Series and Orthogonal Polynomials by : Dunham Jackson
Download or read book Fourier Series and Orthogonal Polynomials written by Dunham Jackson and published by American Mathematical Soc.. This book was released on 1941-12-31 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Fourier Series In Orthogonal Polynomials by : Boris Osilenker
Download or read book Fourier Series In Orthogonal Polynomials written by Boris Osilenker and published by World Scientific. This book was released on 1999-04-01 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Проблемы сходимости ортогональных рядов by : Гыöржи Алекситс
Download or read book Проблемы сходимости ортогональных рядов written by Гыöржи Алекситс and published by . This book was released on 1963 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Orthogonal Series written by B. S. Kashin and published by American Mathematical Soc.. This book was released on 2005-04-26 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Quantum Probability And Related Topics: Qp-pq (Volume Ix) by : Luigi Accardi
Download or read book Quantum Probability And Related Topics: Qp-pq (Volume Ix) written by Luigi Accardi and published by World Scientific. This book was released on 1994-12-16 with total page 427 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum Probability and Related Topics is a series of volumes whose goal is to provide a picture of the state of the art in this rapidly growing field where classical probability, quantum physics and functional analysis merge together in an original synthesis which, for 20 years, has been enriching these three areas with new ideas, techniques and results.
Book Synopsis Orthogonal Polynomials by : Géza Freud
Download or read book Orthogonal Polynomials written by Géza Freud and published by Elsevier. This book was released on 2014-05-17 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: Orthogonal Polynomials contains an up-to-date survey of the general theory of orthogonal polynomials. It deals with the problem of polynomials and reveals that the sequence of these polynomials forms an orthogonal system with respect to a non-negative m-distribution defined on the real numerical axis. Comprised of five chapters, the book begins with the fundamental properties of orthogonal polynomials. After discussing the momentum problem, it then explains the quadrature procedure, the convergence theory, and G. Szego's theory. This book is useful for those who intend to use it as reference for future studies or as a textbook for lecture purposes
Book Synopsis Geometric Aspects of Functional Analysis by : Joram Lindenstrauss
Download or read book Geometric Aspects of Functional Analysis written by Joram Lindenstrauss and published by Birkhäuser. This book was released on 2012-12-06 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the sixth published volume of the Israel Seminar on Geometric Aspects of Functional Analysis. The previous volumes are 1983-84 published privately by Tel Aviv University 1985-86 Springer Lecture Notes, Vol. 1267 1986-87 Springer Lecture Notes, Vol. 1317 1987-88 Springer Lecture Notes, Vol. 1376 1989-90 Springer Lecture Notes, Vol. 1469 As in the previous vC!lumes the central subject of -this volume is Banach space theory in its various aspects. In view of the spectacular development in infinite-dimensional Banach space theory in recent years (like the solution of the hyperplane problem, the unconditional basic sequence problem and the distortion problem in Hilbert space) it is quite natural that the present volume contains substantially more contributions in this direction than the previous volumes. This volume also contains many important contributions in the "traditional directions" of this seminar such as probabilistic methods in functional analysis, non-linear theory, harmonic analysis and especially the local theory of Banach spaces and its connection to classical convexity theory in IRn. The papers in this volume are original research papers and include an invited survey by Alexander Olevskii of Kolmogorov's work on Fourier analysis (which was presented at a special meeting on the occasion of the 90th birthday of A. N. Kol mogorov). We are very grateful to Mrs. M. Hercberg for her generous help in many directions, which made the publication of this volume possible. Joram Lindenstrauss, Vitali Milman 1992-1994 Operator Theory: Advances and Applications, Vol.
Book Synopsis Convergennce Problems of Orthogonal Series by : United States National Bureau of Standards
Download or read book Convergennce Problems of Orthogonal Series written by United States National Bureau of Standards and published by . This book was released on 1961 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Study of the Convergence of Series in Certain Orthogonal Functions by : Reuben Axel Wester
Download or read book Study of the Convergence of Series in Certain Orthogonal Functions written by Reuben Axel Wester and published by . This book was released on 1914 with total page 74 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this present paper we will develop some theorems concerning the degree of convergence of certain series, in particular a Fourier's series, a Legendre's series, and a series of Bessel's functions. Before proceeding directly to the proof of these theorems, however, we will give some theorems showing the conditions under which the Fourier coefficients in the development of a function will converge to zero.
