Convergence And Integrability For Some Classes Of Trigonometric Series
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Convergence And Integrability For Some Classes Of Trigonometric Series
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Author : Živorad Tomovski
language : en
Publisher:
Release Date : 2003
Convergence And Integrability For Some Classes Of Trigonometric Series written by Živorad Tomovski and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Convergence categories.
Dissertationes Mathematicae
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Author :
language : en
Publisher:
Release Date : 2007
Dissertationes Mathematicae written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
Trigonometric Fourier Series And Their Conjugates
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Author : L. Zhizhiashvili
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Trigonometric Fourier Series And Their Conjugates written by L. Zhizhiashvili 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 2012-12-06 with Mathematics categories.
Research in the theory of trigonometric series has been carried out for over two centuries. The results obtained have greatly influenced various fields of mathematics, mechanics, and physics. Nowadays, the theory of simple trigonometric series has been developed fully enough (we will only mention the monographs by Zygmund [15, 16] and Bari [2]). The achievements in the theory of multiple trigonometric series look rather modest as compared to those in the one-dimensional case though multiple trigonometric series seem to be a natural, interesting and promising object of investigation. We should say, however, that the past few decades have seen a more intensive development of the theory in this field. To form an idea about the theory of multiple trigonometric series, the reader can refer to the surveys by Shapiro [1], Zhizhiashvili [16], [46], Golubov [1], D'yachenko [3]. As to monographs on this topic, only that ofYanushauskas [1] is known to me. This book covers several aspects of the theory of multiple trigonometric Fourier series: the existence and properties of the conjugates and Hilbert transforms of integrable functions; convergence (pointwise and in the LP-norm, p > 0) of Fourier series and their conjugates, as well as their summability by the Cesaro (C,a), a> -1, and Abel-Poisson methods; approximating properties of Cesaro means of Fourier series and their conjugates.
Generalized Mathieu Series
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Author : Živorad Tomovski
language : en
Publisher: Springer Nature
Release Date : 2021-11-15
Generalized Mathieu Series written by Živorad Tomovski and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-15 with Mathematics categories.
The Mathieu series is a functional series introduced by Émile Léonard Mathieu for the purposes of his research on the elasticity of solid bodies. Bounds for this series are needed for solving biharmonic equations in a rectangular domain. In addition to Tomovski and his coauthors, Pogany, Cerone, H. M. Srivastava, J. Choi, etc. are some of the known authors who published results concerning the Mathieu series, its generalizations and their alternating variants. Applications of these results are given in classical, harmonic and numerical analysis, analytical number theory, special functions, mathematical physics, probability, quantum field theory, quantum physics, etc. Integral representations, analytical inequalities, asymptotic expansions and behaviors of some classes of Mathieu series are presented in this book. A systematic study of probability density functions and probability distributions associated with the Mathieu series, its generalizations and Planck’s distribution is also presented. The book is addressed at graduate and PhD students and researchers in mathematics and physics who are interested in special functions, inequalities and probability distributions.
Annales Polonici Mathematici
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Author :
language : en
Publisher:
Release Date : 2003
Annales Polonici Mathematici written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
Integrability Theorems For Trigonometric Transforms
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Author : Ralph P.Jr. Boas
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Integrability Theorems For Trigonometric Transforms written by Ralph P.Jr. Boas 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 2012-12-06 with Mathematics categories.
This monograph is areport on the present state of a fairly coherent collection of problems about which a sizeable literature has grown up in recent years. In this literature, some of the problems have, as it happens, been analyzed in great detail, whereas other very similar ones have been treated much more superficially. I have not attempted to improve on the literature by making equally detailed presentations of every topic. I have also not aimed at encyclopedic completeness. I have, however, pointed out some possible generalizations by stating a number of questions; some of these could doubtless be disposed of in a few minutes; some are probably quite difficult. This monograph was written at the suggestion of B. SZ.-NAGY. I take this opportunity of pointing out that his paper [1] inspired the greater part of the material that is presented here; in particular, it contains the happy idea of focusing Y attention on the multipliers nY-i, x- . R. ASKEY, P. HEYWOOD, M. and S. IZUMI, and S. WAINGER have kindly communicated some of their recent results to me before publication. I am indebted for help on various points to L. S. BOSANQUET, S. M. EDMONDS, G. GOES, S. IZUMI, A. ZYGMUND, and especially to R. ASKEY. My work was supported by the National Science Foundation under grants GP-314, GP-2491, GP-3940 and GP-5558. Evanston, Illinois, February, 1967 R. P. Boas, Jr. Contents Notations ... § 1. Introduetion 3 §2. Lemmas .. 7 § 3. Theorems with positive or decreasing functions .
Harmonic Analysis On The Real Line
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Author : Elijah Liflyand
language : en
Publisher: Springer Nature
Release Date : 2021-09-27
Harmonic Analysis On The Real Line written by Elijah Liflyand and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-27 with Mathematics categories.
This book sketches a path for newcomers into the theory of harmonic analysis on the real line. It presents a collection of both basic, well-known and some less known results that may serve as a background for future research around this topic. Many of these results are also a necessary basis for multivariate extensions. An extensive bibliography, as well as hints to open problems are included. The book can be used as a skeleton for designing certain special courses, but it is also suitable for self-study.
Fourier Analysis
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Author : William O. Bray
language : en
Publisher: CRC Press
Release Date : 2020-12-17
Fourier Analysis written by William O. Bray and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-17 with Mathematics categories.
Providing complete expository and research papers on the geometric and analytic aspects of Fourier analysis, this work discusses new approaches to classical problems in the theory of trigonometric series, singular integrals/pseudo-differential operators, Fourier analysis on various groups, numerical aspects of Fourier analysis and their applications, wavelets and more.
Probability Theory Function Theory Mechanics
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Author : I︠U︡riĭ Vasilʹevich Prokhorov
language : en
Publisher: American Mathematical Soc.
Release Date : 1990
Probability Theory Function Theory Mechanics written by I︠U︡riĭ Vasilʹevich Prokhorov 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 1990 with Mathematics categories.
This is a translation of the fifth and final volume in a special cycle of publications in commemoration of the 50th anniversary of the Steklov Mathematical Institute of the Academy of Sciences in the USSR. The purpose of the special cycle was to present surveys of work on certain important trends and problems pursued at the Institute. Because the choice of the form and character of the surveys were left up to the authors, the surveys do not necessarily form a comprehensive overview, but rather represent the authors' perspectives on the important developments.
Integral And Discrete Transforms With Applications And Error Analysis
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Author : Abdul Jerri
language : en
Publisher: CRC Press
Release Date : 2021-11-19
Integral And Discrete Transforms With Applications And Error Analysis written by Abdul Jerri and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-19 with Mathematics categories.
This reference/text desribes the basic elements of the integral, finite, and discrete transforms - emphasizing their use for solving boundary and initial value problems as well as facilitating the representations of signals and systems.;Proceeding to the final solution in the same setting of Fourier analysis without interruption, Integral and Discrete Transforms with Applications and Error Analysis: presents the background of the FFT and explains how to choose the appropriate transform for solving a boundary value problem; discusses modelling of the basic partial differential equations, as well as the solutions in terms of the main special functions; considers the Laplace, Fourier, and Hankel transforms and their variations, offering a more logical continuation of the operational method; covers integral, discrete, and finite transforms and trigonometric Fourier and general orthogonal series expansion, providing an application to signal analysis and boundary-value problems; and examines the practical approximation of computing the resulting Fourier series or integral representation of the final solution and treats the errors incurred.;Containing many detailed examples and numerous end-of-chapter exercises of varying difficulty for each section with answers, Integral and Discrete Transforms with Applications and Error Analysis is a thorough reference for analysts; industrial and applied mathematicians; electrical, electronics, and other engineers; and physicists and an informative text for upper-level undergraduate and graduate students in these disciplines.