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On The Strong Summability And Approximation Of Fourier Series
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Book Synopsis Functional Analysis and Approximation by : P.L. Butzer
Download or read book Functional Analysis and Approximation written by P.L. Butzer and published by Birkhäuser. This book was released on 2013-03-07 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: These Proceedings form a record of the lectures presented at the interna tional Conference on Functional Analysis and Approximation held at the Ober wolfach Mathematical Research Institute, August 9-16, 1980. They include 33 of the 38 invited conference papers, as well as three papers subsequently submitted in writing. Further, there is a report devoted to new and unsolved problems, based on two special sessions of the conference. The present volume is the sixth Oberwolfach Conference in Birkhauser's ISNM series to be edited at Aachen *. It is once again devoted to more significant results obtained in the wide areas of approximation theory, harmonic analysis, functional analysis, and operator theory during the past three years. Many of the papers solicited not only outline fundamental advances in their fields but also focus on interconnections between the various research areas. The papers in the present volume have been grouped into nine chapters. Chapter I, on operator theory, deals with maps on positive semidefinite opera tors, spectral bounds of semigroup operators, evolution equations of diffusion type, the spectral theory of propagators, and generalized inverses. Chapter II, on functional analysis, contains papers on modular approximation, interpolation spaces, and unconditional bases.
Book Synopsis Fourier Analysis and Approximation of Functions by : Roald M. Trigub
Download or read book Fourier Analysis and Approximation of Functions written by Roald M. Trigub and published by Springer Science & Business Media. This book was released on 2012-11-07 with total page 595 pages. Available in PDF, EPUB and Kindle. Book excerpt: In Fourier Analysis and Approximation of Functions basics of classical Fourier Analysis are given as well as those of approximation by polynomials, splines and entire functions of exponential type. In Chapter 1 which has an introductory nature, theorems on convergence, in that or another sense, of integral operators are given. In Chapter 2 basic properties of simple and multiple Fourier series are discussed, while in Chapter 3 those of Fourier integrals are studied. The first three chapters as well as partially Chapter 4 and classical Wiener, Bochner, Bernstein, Khintchin, and Beurling theorems in Chapter 6 might be interesting and available to all familiar with fundamentals of integration theory and elements of Complex Analysis and Operator Theory. Applied mathematicians interested in harmonic analysis and/or numerical methods based on ideas of Approximation Theory are among them. In Chapters 6-11 very recent results are sometimes given in certain directions. Many of these results have never appeared as a book or certain consistent part of a book and can be found only in periodics; looking for them in numerous journals might be quite onerous, thus this book may work as a reference source. The methods used in the book are those of classical analysis, Fourier Analysis in finite-dimensional Euclidean space Diophantine Analysis, and random choice.
Book Synopsis Convergence and Summability of Fourier Transforms and Hardy Spaces by : Ferenc Weisz
Download or read book Convergence and Summability of Fourier Transforms and Hardy Spaces written by Ferenc Weisz and published by Birkhäuser. This book was released on 2017-12-27 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book investigates the convergence and summability of both one-dimensional and multi-dimensional Fourier transforms, as well as the theory of Hardy spaces. To do so, it studies a general summability method known as theta-summation, which encompasses all the well-known summability methods, such as the Fejér, Riesz, Weierstrass, Abel, Picard, Bessel and Rogosinski summations. Following on the classic books by Bary (1964) and Zygmund (1968), this is the first book that considers strong summability introduced by current methodology. A further unique aspect is that the Lebesgue points are also studied in the theory of multi-dimensional summability. In addition to classical results, results from the past 20-30 years – normally only found in scattered research papers – are also gathered and discussed, offering readers a convenient “one-stop” source to support their work. As such, the book will be useful for researchers, graduate and postgraduate students alike.
Book Synopsis Lebesgue Points and Summability of Higher Dimensional Fourier Series by : Ferenc Weisz
Download or read book Lebesgue Points and Summability of Higher Dimensional Fourier Series written by Ferenc Weisz and published by Springer Nature. This book was released on 2021-06-12 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents the summability of higher dimensional Fourier series, and generalizes the concept of Lebesgue points. Focusing on Fejér and Cesàro summability, as well as theta-summation, readers will become more familiar with a wide variety of summability methods. Within the theory of higher dimensional summability of Fourier series, the book also provides a much-needed simple proof of Lebesgue’s theorem, filling a gap in the literature. Recent results and real-world applications are highlighted as well, making this a timely resource. The book is structured into four chapters, prioritizing clarity throughout. Chapter One covers basic results from the one-dimensional Fourier series, and offers a clear proof of the Lebesgue theorem. In Chapter Two, convergence and boundedness results for the lq-summability are presented. The restricted and unrestricted rectangular summability are provided in Chapter Three, as well as the sufficient and necessary condition for the norm convergence of the rectangular theta-means. Chapter Four then introduces six types of Lebesgue points for higher dimensional functions. Lebesgue Points and Summability of Higher Dimensional Fourier Series will appeal to researchers working in mathematical analysis, particularly those interested in Fourier and harmonic analysis. Researchers in applied fields will also find this useful.
Book Synopsis Classification and Approximation of Periodic Functions by : A.I. Stepanets
Download or read book Classification and Approximation of Periodic Functions written by A.I. Stepanets and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph proposes a new classification of periodic functions, based on the concept of generalized derivative, defined by introducing multiplicators and shifts of the argument into the Fourier series of the original function. This approach permits the classification of a wide range of functions, including those of which the Fourier series may diverge in integral metric, smooth functions, and infinitely differentiable functions, including analytical and entire ones. These newly introduced classes are then investigated using the traditional problems of the theory of approximation. The results thus obtained offer a new way to look at classical statements for the approximation of differentiable functions, and suggest possibilities to discover new effects. Audience: valuable reading for experts in the field of mathematical analysis and researchers and graduate students interested in the applications of the theory of approximation and Fourier series.
Book Synopsis Topics in Fourier Analysis and Function Spaces by : Hans-Jurgen Schmeisser
Download or read book Topics in Fourier Analysis and Function Spaces written by Hans-Jurgen Schmeisser and published by . This book was released on 1987-03-11 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: A book dealing with several classes of Besov-Hardy-Sobolev function spaces on the Euclidean n-space and the n-torus. Periodic, weighted and anisotropic spaces are discussed, as well as spaces in which properties of dominating mixed smoothness predominate.
Book Synopsis Martingale Hardy Spaces and Summability of One-Dimensional Vilenkin-Fourier Series by : Lars-Erik Persson
Download or read book Martingale Hardy Spaces and Summability of One-Dimensional Vilenkin-Fourier Series written by Lars-Erik Persson and published by Springer Nature. This book was released on 2022-11-22 with total page 633 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses, develops and applies the theory of Vilenkin-Fourier series connected to modern harmonic analysis. The classical theory of Fourier series deals with decomposition of a function into sinusoidal waves. Unlike these continuous waves the Vilenkin (Walsh) functions are rectangular waves. Such waves have already been used frequently in the theory of signal transmission, multiplexing, filtering, image enhancement, code theory, digital signal processing and pattern recognition. The development of the theory of Vilenkin-Fourier series has been strongly influenced by the classical theory of trigonometric series. Because of this it is inevitable to compare results of Vilenkin-Fourier series to those on trigonometric series. There are many similarities between these theories, but there exist differences also. Much of these can be explained by modern abstract harmonic analysis, which studies orthonormal systems from the point of view of the structure of a topological group. The first part of the book can be used as an introduction to the subject, and the following chapters summarize the most recent research in this fascinating area and can be read independently. Each chapter concludes with historical remarks and open questions. The book will appeal to researchers working in Fourier and more broad harmonic analysis and will inspire them for their own and their students' research. Moreover, researchers in applied fields will appreciate it as a sourcebook far beyond the traditional mathematical domains.
Book Synopsis Methods of Approximation Theory by : Alexander I. Stepanets
Download or read book Methods of Approximation Theory written by Alexander I. Stepanets and published by Walter de Gruyter. This book was released on 2011-12-22 with total page 941 pages. Available in PDF, EPUB and Kindle. Book excerpt: The key point of the monograph is the classification of periodic functions introduced by the author and developed methods that enable one to solve, within the framework of a common approach, traditional problems of approximation theory for large collections of periodic functions. The main results are fairly complete and are presented in the form of either exact or asymptotically exact equalities. The present monograph is, in many respects, a store of knowledge accumulated in approximation theory by the beginning of the third millennium and serving for its further development.
Book Synopsis Operators, Inequalities and Approximation by : Binod Chandra Tripathy
Download or read book Operators, Inequalities and Approximation written by Binod Chandra Tripathy and published by Springer Nature. This book was released on with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Thirteen Papers in Analysis by : R. R. Suncheleev
Download or read book Thirteen Papers in Analysis written by R. R. Suncheleev and published by American Mathematical Soc.. This book was released on 1986 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis On approximation theory by : Jacob Korevaar
Download or read book On approximation theory written by Jacob Korevaar and published by Springer. This book was released on 2013-12-14 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Abstract Spaces and Approximation / Abstrakte Räume und Approximation by : Butzer
Download or read book Abstract Spaces and Approximation / Abstrakte Räume und Approximation written by Butzer and published by Birkhäuser. This book was released on 2013-11-21 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present conference took place at Oberwolfach, July 18-27, 1968, as a direct follow-up on a meeting on Approximation Theory [1] held there from August 4-10, 1963. The emphasis was on theoretical aspects of approximation, rather than the numerical side. Particular importance was placed on the related fields of functional analysis and operator theory. Thirty-nine papers were presented at the conference and one more was subsequently submitted in writing. All of these are included in these proceedings. In addition there is areport on new and unsolved problems based upon a special problem session and later communications from the partici pants. A special role is played by the survey papers also presented in full. They cover a broad range of topics, including invariant subspaces, scattering theory, Wiener-Hopf equations, interpolation theorems, contraction operators, approximation in Banach spaces, etc. The papers have been classified according to subject matter into five chapters, but it needs little emphasis that such thematic groupings are necessarily arbitrary to some extent. The Proceedings are dedicated to the memory of Jean Favard. It was Favard who gave the Oberwolfach Conference of 1963 a special impetus and whose absence was deeply regretted this time. An appreciation of his li fe and contributions was presented verbally by Georges Alexits, while the written version bears the signa tures of both Alexits and Marc Zamansky. Our particular thanks are due to E.
Book Synopsis Approximation Theory by : Zbigniew Ciesielski
Download or read book Approximation Theory written by Zbigniew Ciesielski and published by . This book was released on 1979 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Recent Advances in Harmonic Analysis and Applications by : Dmitriy Bilyk
Download or read book Recent Advances in Harmonic Analysis and Applications written by Dmitriy Bilyk and published by Springer Science & Business Media. This book was released on 2012-10-16 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent Advances in Harmonic Analysis and Applications features selected contributions from the AMS conference which took place at Georgia Southern University, Statesboro in 2011 in honor of Professor Konstantin Oskolkov's 65th birthday. The contributions are based on two special sessions, namely "Harmonic Analysis and Applications" and "Sparse Data Representations and Applications." Topics covered range from Banach space geometry to classical harmonic analysis and partial differential equations. Survey and expository articles by leading experts in their corresponding fields are included, and the volume also features selected high quality papers exploring new results and trends in Muckenhoupt-Sawyer theory, orthogonal polynomials, trigonometric series, approximation theory, Bellman functions and applications in differential equations. Graduate students and researchers in analysis will be particularly interested in the articles which emphasize remarkable connections between analysis and analytic number theory. The readers will learn about recent mathematical developments and directions for future work in the unexpected and surprising interaction between abstract problems in additive number theory and experimentally discovered optical phenomena in physics. This book will be useful for number theorists, harmonic analysts, algorithmists in multi-dimensional signal processing and experts in physics and partial differential equations.
Book Synopsis A Treatise on Trigonometric Series by : N. K. Bary
Download or read book A Treatise on Trigonometric Series written by N. K. Bary and published by Elsevier. This book was released on 2014-05-12 with total page 578 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Treatise on Trigonometric Series, Volume 1 deals comprehensively with the classical theory of Fourier series. This book presents the investigation of best approximations of functions by trigonometric polynomials. Organized into six chapters, this volume begins with an overview of the fundamental concepts and theorems in the theory of trigonometric series, which play a significant role in mathematics and in many of its applications. This text then explores the properties of the Fourier coefficient function and estimates the rate at which its Fourier coefficients tend to zero. Other chapters consider some tests for the convergence of a Fourier series at a given point. This book discusses as well the conditions under which the series does converge uniformly. The final chapter deals with adjustment of a summable function outside a given perfect set. This book is a valuable resource for advanced students and research workers. Mathematicians will also find this book useful.
Book Synopsis Advanced Mathematical Techniques in Engineering Sciences by : Mangey Ram
Download or read book Advanced Mathematical Techniques in Engineering Sciences written by Mangey Ram and published by CRC Press. This book was released on 2018-05-04 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of this book is to publish the latest mathematical techniques, research, and developments in engineering. This book includes a comprehensive range of mathematics applied in engineering areas for different tasks. Various mathematical tools, techniques, strategies, and methods in engineering applications are covered in each chapter. Mathematical techniques are the strength of engineering sciences and form the common foundation of all novel disciplines within the field. Advanced Mathematical Techniques in Engineering Sciences provides an ample range of mathematical tools and techniques applied across various fields of engineering sciences. Using this book, engineers will gain a greater understanding of the practical applications of mathematics in engineering sciences. Features Covers the mathematical techniques applied in engineering sciences Focuses on the latest research in the field of engineering applications Provides insights on an international and transnational scale Offers new studies and research in modeling and simulation
Book Synopsis Summability of Multi-Dimensional Fourier Series and Hardy Spaces by : Ferenc Weisz
Download or read book Summability of Multi-Dimensional Fourier Series and Hardy Spaces written by Ferenc Weisz and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: The history of martingale theory goes back to the early fifties when Doob [57] pointed out the connection between martingales and analytic functions. On the basis of Burkholder's scientific achievements the mar tingale theory can perfectly well be applied in complex analysis and in the theory of classical Hardy spaces. This connection is the main point of Durrett's book [60]. The martingale theory can also be well applied in stochastics and mathematical finance. The theories of the one-parameter martingale and the classical Hardy spaces are discussed exhaustively in the literature (see Garsia [83], Neveu [138], Dellacherie and Meyer [54, 55], Long [124], Weisz [216] and Duren [59], Stein [193, 194], Stein and Weiss [192], Lu [125], Uchiyama [205]). The theory of more-parameter martingales and martingale Hardy spaces is investigated in Imkeller [107] and Weisz [216]. This is the first mono graph which considers the theory of more-parameter classical Hardy spaces. The methods of proofs for one and several parameters are en tirely different; in most cases the theorems stated for several parameters are much more difficult to verify. The so-called atomic decomposition method that can be applied both in the one-and more-parameter cases, was considered for martingales by the author in [216].
