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Author : Georgi P. Tolstov
ISBN : 9780486141749
Genre : Mathematics
File Size : 72.69 MB
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This reputable translation covers trigonometric Fourier series, orthogonal systems, double Fourier series, Bessel functions, the Eigenfunction method and its applications to mathematical physics, operations on Fourier series, and more. Over 100 problems. 1962 edition.

This is a concise introduction to Fourier series covering history, major themes, theorems, examples, and applications. It can be used for self study, or to supplement undergraduate courses on mathematical analysis. Beginning with a brief summary of the rich history of the subject over three centuries, the reader will appreciate how a mathematical theory develops in stages from a practical problem (such as conduction of heat) to an abstract theory dealing with concepts such as sets, functions, infinity, and convergence. The abstract theory then provides unforeseen applications in diverse areas. Exercises of varying difficulty are included throughout to test understanding. A broad range of applications are also covered, and directions for further reading and research are provided, along with a chapter that provides material at a more advanced level suitable for graduate students.

Author : Juan Arias de Reyna
ISBN : 3540432701
Genre : Mathematics
File Size : 31.80 MB
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This book contains a detailed exposition of Carleson-Hunt theorem following the proof of Carleson: to this day this is the only one giving better bounds. It points out the motivation of every step in the proof. Thus the Carleson-Hunt theorem becomes accessible to any analyst.The book also contains the first detailed exposition of the fine results of Hunt, Sjölin, Soria, etc on the convergence of Fourier Series. Its final chapters present original material. With both Fefferman's proof and the recent one of Lacey and Thiele in print, it becomes more important than ever to understand and compare these two related proofs with that of Carleson and Hunt. These alternative proofs do not yield all the results of the Carleson-Hunt proof. The intention of this monograph is to make Carleson's proof accessible to a wider audience, and to explain its consequences for the pointwise convergence of Fourier series for functions in spaces near $äcal Lü^1$, filling a well-known gap in the literature.

Author : Dunham Jackson
ISBN : 0486438082
Genre : Mathematics
File Size : 55.71 MB
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This text illustrates the fundamental simplicity of the properties of orthogonal functions and their developments in related series. Begins with a definition and explanation of the elements of Fourier series, and examines Legendre polynomials and Bessel functions. Also includes Pearson frequency functions and chapters on orthogonal, Jacobi, Hermite, and Laguerre polynomials, more. 1941 edition.

Author : Robert M. Young
ISBN : 0127729550
Genre : Mathematics
File Size : 32.88 MB
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An Introduction to Non-Harmonic Fourier Series, Revised Edition is an update of a widely known and highly respected classic textbook. Throughout the book, material has also been added on recent developments, including stability theory, the frame radius, and applications to signal analysis and the control of partial differential equations.

Author : Phil Dyke
ISBN : 1852330155
Genre : Mathematics
File Size : 27.39 MB
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This introduction to Laplace transforms and Fourier series is aimed at second year students in applied mathematics. It is unusual in treating Laplace transforms at a relatively simple level with many examples. Mathematics students do not usually meet this material until later in their degree course but applied mathematicians and engineers need an early introduction. Suitable as a course text, it will also be of interest to physicists and engineers as supplementary material.

Author : Michael B. Marcus
ISBN : 0691082928
Genre : Mathematics
File Size : 28.50 MB
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The changes to U.S. immigration law that were instituted in 1965 have led to an influx of West African immigrants to New York, creating an enclave Harlem residents now call ''Little Africa.'' These immigrants are immediately recognizable as African in their wide-sleeved robes and tasseled hats, but most native-born members of the community are unaware of the crucial role Islam plays in immigrants' lives. Zain Abdullah takes us inside the lives of these new immigrants and shows how they deal with being a double minority in a country where both blacks and Muslims are stigmatized. Dealing with this dual identity, Abdullah discovers, is extraordinarily complex. Some longtime residents embrace these immigrants and see their arrival as an opportunity to reclaim their African heritage, while others see the immigrants as scornful invaders. In turn, African immigrants often take a particularly harsh view of their new neighbors, buying into the worst stereotypes about American-born blacks being lazy and incorrigible. And while there has long been a large Muslim presence in Harlem, and residents often see Islam as a force for social good, African-born Muslims see their Islamic identity disregarded by most of their neighbors. Abdullah weaves together the stories of these African Muslims to paint a fascinating portrait of a community's efforts to carve out space for itself in a new country. -- Book jacket.

Author : L. Zhizhiashvili
ISBN : 0792340884
Genre : Mathematics
File Size : 73.31 MB
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This book presents in a coherent way the results obtained in the following aspects of the theory of multiple trigonometric Fourier series: the existence and properties of the conjugates and Hilbert transforms of integrable functions of several variables; convergence of Fourier series and their conjugates, as well as their summability by Cesàro and Abel-Poisson methods; and approximating properties of Cesàro means of Fourier series and their conjugates. Special emphasis is put on new effects which arise from dealing with multiple series and which are not inherent in the one-dimensional case. Unsolved problems are formulated separately. Audience: This volume will prove useful to both graduate students and research workers in the field of Fourier analysis, approximations and expansions, integral transforms, and operational calculus.

Author : Sergei Suslov
ISBN : 1402012217
Genre : Mathematics
File Size : 50.79 MB
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It was with the publication of Norbert Wiener's book ''The Fourier In tegral and Certain of Its Applications" [165] in 1933 by Cambridge Univer sity Press that the mathematical community came to realize that there is an alternative approach to the study of c1assical Fourier Analysis, namely, through the theory of c1assical orthogonal polynomials. Little would he know at that time that this little idea of his would help usher in a new and exiting branch of c1assical analysis called q-Fourier Analysis. Attempts at finding q-analogs of Fourier and other related transforms were made by other authors, but it took the mathematical insight and instincts of none other then Richard Askey, the grand master of Special Functions and Orthogonal Polynomials, to see the natural connection between orthogonal polynomials and a systematic theory of q-Fourier Analysis. The paper that he wrote in 1993 with N. M. Atakishiyev and S. K Suslov, entitled "An Analog of the Fourier Transform for a q-Harmonic Oscillator" [13], was probably the first significant publication in this area. The Poisson k~rnel for the contin uous q-Hermite polynomials plays a role of the q-exponential function for the analog of the Fourier integral under considerationj see also [14] for an extension of the q-Fourier transform to the general case of Askey-Wilson polynomials. (Another important ingredient of the q-Fourier Analysis, that deserves thorough investigation, is the theory of q-Fourier series.

Fourier Series and Transforms, a software and text package, complements standard textbooks and lecture courses by providing a solid overview of the topic. The software provides more extensive illustrations than a conventional text with interactive programs that have been designed to be open to modifications. The emphasis on qualitative aspects and flexibility with regard to program modification make the package useful to a wide range of students. The book assumes some mathematical expertise as well as basic computer language knowledge.

Author : Godfrey Harold Hardy
ISBN : 9780486406817
Genre : Mathematics
File Size : 54.34 MB
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Geared toward mathematicians already familiar with the elements of Lebesgue's theory of integration, this classic graduate-level text begins with a brief introduction to some generalities of trigonometrical series. Discussions of the Fourier series in Hilbert space lead to an examination of further properties of trigonometrical Fourier series and related subjects. 1956 edition.

Author : Harry F. Davis
ISBN : 9780486140735
Genre : Mathematics
File Size : 43.49 MB
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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.

Author : J. Ray Hanna
ISBN : 9780486466736
Genre : Mathematics
File Size : 73.23 MB
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This volume introduces Fourier and transform methods for solutions to boundary value problems associated with natural phenomena. Unlike most treatments, it emphasizes basic concepts and techniques rather than theory. Many of the exercises include solutions, with detailed outlines that make it easy to follow the appropriate sequence of steps. 1990 edition.

Author : Ferenc Weisz
ISBN : 1402005644
Genre : Mathematics
File Size : 55.41 MB
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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].