Author: Harry Floyd Davis
Publisher:
ISBN:
Category :
Languages : en
Pages : 415

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Book Description

Author: Harry F. Davis
Publisher: Courier Corporation
ISBN: 9780486659732
Category : Mathematics
Languages : en
Pages : 436

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Book Description
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: Dunham Jackson
Publisher: American Mathematical Soc.
ISBN: 1614440069
Category : Fourier series
Languages : en
Pages : 234

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Book Description
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.

Author: Dunham Jackson
Publisher:
ISBN:
Category : Fourier series
Languages : en
Pages : 256

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Book Description

Author: Boris Osilenker
Publisher: World Scientific
ISBN: 9789810237875
Category : Mathematics
Languages : en
Pages : 304

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Book Description
This book presents a systematic coarse on general orthogonal polynomials and Fourie 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 L(2)micro; 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 and physicists) whose work involves function theory, functional analysis, harmonic analysis and approximation theory.

Author: A. Olevskii
Publisher: Springer
ISBN: 9783642660580
Category : Mathematics
Languages : en
Pages : 138

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Book Description
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 {

Author: Giovanni Sansone
Publisher:
ISBN:
Category : Functions, Orthogonal
Languages : en
Pages : 440

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Book Description
Highly regarded treatise contains a rich compilation of general results and convenient criteria concerning Fourier series, Legendre series, Laguerre and Hermite polynomials. Until publication of this book, much of the material had not been available in English. First paperback edition. Translated by Ainsley H. Diamond. Foreword. Bibliography. 14 black-and-white illustrations.

Author: Gilbert G. Walter
Publisher: CRC Press
ISBN: 9780849378782
Category : Mathematics
Languages : en
Pages : 264

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Book Description
This book makes accessible to both mathematicians and engineers important elements of the theory, construction, and application of orthogonal wavelets. It is integrated with more traditional orthogonal series, such as Fourier series and orthogonal polynomials. It treats the interaction of both with generalized functions (delta functions), which have played an important part in engineering theory but whose rules are often vaguely presented. Unlike most other books that are excessively technical, this text/reference presents the basic concepts and examples in a readable form. Much of the material on wavelets has not appeared previously in book form. Applications to statistics, sampling theorems, and stochastic processes are given. In particular, the close affinity between wavelets and sampling theorems is explained and developed.

Author: A. M. Olevskij
Publisher:
ISBN:
Category :
Languages : de
Pages : 0

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Book Description

Author: Howard J. Wilcox
Publisher: Courier Corporation
ISBN: 0486137473
Category : Mathematics
Languages : en
Pages : 194

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Book Description
This book arose out of the authors' desire to present Lebesgue integration and Fourier series on an undergraduate level, since most undergraduate texts do not cover this material or do so in a cursory way. The result is a clear, concise, well-organized introduction to such topics as the Riemann integral, measurable sets, properties of measurable sets, measurable functions, the Lebesgue integral, convergence and the Lebesgue integral, pointwise convergence of Fourier series and other subjects. The authors not only cover these topics in a useful and thorough way, they have taken pains to motivate the student by keeping the goals of the theory always in sight, justifying each step of the development in terms of those goals. In addition, whenever possible, new concepts are related to concepts already in the student's repertoire. Finally, to enable readers to test their grasp of the material, the text is supplemented by numerous examples and exercises. Mathematics students as well as students of engineering and science will find here a superb treatment, carefully thought out and well presented , that is ideal for a one semester course. The only prerequisite is a basic knowledge of advanced calculus, including the notions of compactness, continuity, uniform convergence and Riemann integration.