Download or read book Absolute Summability of Fourier Series and Orthogonal Series written by Y. Okuyama and published by Springer. This book was released on 2006-12-08 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Absolute Summability of Fourier Series and Orthogonal Series written by and published by . This book was released on 1984 with total page 117 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Summation of the Fourier Series of Orthogonal Functions written by Jian'gong Chen and published by . This book was released on 1957 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Sequences Summability and Fourier Analysis written by S. Nanda and published by Alpha Science Int'l Ltd.. This book was released on 2005 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sequences, Summability and Fourier Analysis deals with various aspects of summability, a major branch of analysis. The subject grew extensively during the twentieth century through the contribution of eminent analysts, but there are numerous unsolved problems, which still baffle the present-day scholars, as the application side has been poorly attended to. This volume contains original research articles, many valuable survey articles on approximation theory, multivalent functions, almost convergence and absolute almost convergence, Tauberian theorems, Köthe-Toeplitz duals of sequence spaces, random Fourier series, stochastic integrals, interpolative subspaces of Banach space, metric transformations in sequence spaces, absolute summability and Nörlund summability.

Download or read book Fourier Series and Orthogonal Functions written by Harry F. Davis and published by Courier Corporation. This book was released on 1989-01-01 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: An incisive text combining theory and practical example to introduce Fourier series, orthogonal functions and applications of the Fourier method to boundary-value problems. Includes 570 exercises. Answers and notes.

Download or read book An Introduction to Fourier Series and Integrals written by Robert T. Seeley and published by Courier Corporation. This book was released on 2014-02-20 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: A compact, sophomore-to-senior-level guide, Dr. Seeley's text introduces Fourier series in the way that Joseph Fourier himself used them: as solutions of the heat equation in a disk. Emphasizing the relationship between physics and mathematics, Dr. Seeley focuses on results of greatest significance to modern readers. Starting with a physical problem, Dr. Seeley sets up and analyzes the mathematical modes, establishes the principal properties, and then proceeds to apply these results and methods to new situations. The chapter on Fourier transforms derives analogs of the results obtained for Fourier series, which the author applies to the analysis of a problem of heat conduction. Numerous computational and theoretical problems appear throughout the text.

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.

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 2004-09-07 with total page 610 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.

Download or read book The Strong Summability of Fourier Series written by Edgar Clarence Smith (Jr.) and published by . This book was released on 1950 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Note on the Absolute Summability of Fourier Series written by Fu Traing Wang and published by . This book was released on 1941 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Introduction to the Theory of Fourier s Series and Integrals written by Horatio Scott Carslaw and published by . This book was released on 1921 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Principles of Fourier Analysis written by Kenneth B. Howell and published by CRC Press. This book was released on 2001-05-18 with total page 791 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fourier analysis is one of the most useful and widely employed sets of tools for the engineer, the scientist, and the applied mathematician. As such, students and practitioners in these disciplines need a practical and mathematically solid introduction to its principles. They need straightforward verifications of its results and formulas, and they need clear indications of the limitations of those results and formulas. Principles of Fourier Analysis furnishes all this and more. It provides a comprehensive overview of the mathematical theory of Fourier analysis, including the development of Fourier series, "classical" Fourier transforms, generalized Fourier transforms and analysis, and the discrete theory. Much of the author's development is strikingly different from typical presentations. His approach to defining the classical Fourier transform results in a much cleaner, more coherent theory that leads naturally to a starting point for the generalized theory. He also introduces a new generalized theory based on the use of Gaussian test functions that yields an even more general -yet simpler -theory than usually presented. Principles of Fourier Analysis stimulates the appreciation and understanding of the fundamental concepts and serves both beginning students who have seen little or no Fourier analysis as well as the more advanced students who need a deeper understanding. Insightful, non-rigorous derivations motivate much of the material, and thought-provoking examples illustrate what can go wrong when formulas are misused. With clear, engaging exposition, readers develop the ability to intelligently handle the more sophisticated mathematics that Fourier analysis ultimately requires.

Download or read book Introduction to Fourier Series written by Rupert Lasser and published by CRC Press. This book was released on 1996-02-08 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work addresses all of the major topics in Fourier series, emphasizing the concept of approximate identities and presenting applications, particularly in time series analysis. It stresses throughout the idea of homogenous Banach spaces and provides recent results. Techniques from functional analysis and measure theory are utilized.;College and university bookstores may order five or more copies at a special student price, available on request from Marcel Dekker, Inc.

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 2018-01-18 with total page 0 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.

Download or read book Fourier Series with Respect to General Orthogonal Systems written by A. Olevskii and published by Springer. This book was released on 2011-11-15 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fundamental problem of the theory of Fourier series consists of the investigation of the connections between the metric properties of the function expanded, the behavior of its Fourier coefficients {cn} with respect to an ortho normal system of functions {

Download or read book Fourier Series a Modern Introduction written by Robert E. Edwards and published by . This book was released on 1979 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Introduction to Fourier Analysis and Wavelets written by Mark A. Pinsky and published by American Mathematical Society. This book was released on 2023-12-21 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a concrete introduction to a number of topics in harmonic analysis, accessible at the early graduate level or, in some cases, at an upper undergraduate level. Necessary prerequisites to using the text are rudiments of the Lebesgue measure and integration on the real line. It begins with a thorough treatment of Fourier series on the circle and their applications to approximation theory, probability, and plane geometry (the isoperimetric theorem). Frequently, more than one proof is offered for a given theorem to illustrate the multiplicity of approaches. The second chapter treats the Fourier transform on Euclidean spaces, especially the author's results in the three-dimensional piecewise smooth case, which is distinct from the classical Gibbs–Wilbraham phenomenon of one-dimensional Fourier analysis. The Poisson summation formula treated in Chapter 3 provides an elegant connection between Fourier series on the circle and Fourier transforms on the real line, culminating in Landau's asymptotic formulas for lattice points on a large sphere. Much of modern harmonic analysis is concerned with the behavior of various linear operators on the Lebesgue spaces $L^p(mathbb{R}^n)$. Chapter 4 gives a gentle introduction to these results, using the Riesz–Thorin theorem and the Marcinkiewicz interpolation formula. One of the long-time users of Fourier analysis is probability theory. In Chapter 5 the central limit theorem, iterated log theorem, and Berry–Esseen theorems are developed using the suitable Fourier-analytic tools. The final chapter furnishes a gentle introduction to wavelet theory, depending only on the $L_2$ theory of the Fourier transform (the Plancherel theorem). The basic notions of scale and location parameters demonstrate the flexibility of the wavelet approach to harmonic analysis. The text contains numerous examples and more than 200 exercises, each located in close proximity to the related theoretical material.