Fourier Series And Orthogonal Functions

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Fourier Series and Orthogonal Functions

Author : Harry F. Davis
Publisher : Courier Corporation
ISBN 13 : 0486140733
Total Pages : 436 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Fourier Series and Orthogonal Functions by : Harry F. Davis

Download or read book Fourier Series and Orthogonal Functions written by Harry F. Davis and published by Courier Corporation. This book was released on 2012-09-05 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: This incisive text deftly combines both theory and practical example to introduce and explore Fourier series and orthogonal functions and applications of the Fourier method to the solution of boundary-value problems. Directed to advanced undergraduate and graduate students in mathematics as well as in physics and engineering, the book requires no prior knowledge of partial differential equations or advanced vector analysis. Students familiar with partial derivatives, multiple integrals, vectors, and elementary differential equations will find the text both accessible and challenging. The first three chapters of the book address linear spaces, orthogonal functions, and the Fourier series. Chapter 4 introduces Legendre polynomials and Bessel functions, and Chapter 5 takes up heat and temperature. The concluding Chapter 6 explores waves and vibrations and harmonic analysis. Several topics not usually found in undergraduate texts are included, among them summability theory, generalized functions, and spherical harmonics. Throughout the text are 570 exercises devised to encourage students to review what has been read and to apply the theory to specific problems. Those preparing for further study in functional analysis, abstract harmonic analysis, and quantum mechanics will find this book especially valuable for the rigorous preparation it provides. Professional engineers, physicists, and mathematicians seeking to extend their mathematical horizons will find it an invaluable reference as well.

Fourier Series and Orthogonal Polynomials

Author : Dunham Jackson
Publisher : American Mathematical Soc.
ISBN 13 : 1614440069
Total Pages : 234 pages
Book Rating : 4.6/5 (144 download)

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Book Synopsis Fourier Series and Orthogonal Polynomials by : Dunham Jackson

Download or read book Fourier Series and Orthogonal Polynomials written by Dunham Jackson and published by American Mathematical Soc.. This book was released on 1941-12-31 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Fourier Series and Orthogonal Functions

Author : Harry Floyd Davis
Publisher :
ISBN 13 :
Total Pages : 415 pages
Book Rating : 4.:/5 (257 download)

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Book Synopsis Fourier Series and Orthogonal Functions by : Harry Floyd Davis

Download or read book Fourier Series and Orthogonal Functions written by Harry Floyd Davis and published by . This book was released on 1966 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Fourier Series and Orthogonal Polynomials

Author : Dunham Jackson
Publisher :
ISBN 13 :
Total Pages : 256 pages
Book Rating : 4.:/5 (318 download)

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Book Synopsis Fourier Series and Orthogonal Polynomials by : Dunham Jackson

Download or read book Fourier Series and Orthogonal Polynomials written by Dunham Jackson and published by . This book was released on 1941 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Fourier Series with Respect to General Orthogonal Systems

Author : A. Olevskii
Publisher : Springer
ISBN 13 : 9783642660580
Total Pages : 138 pages
Book Rating : 4.6/5 (65 download)

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Book Synopsis Fourier Series with Respect to General Orthogonal Systems by : A. Olevskii

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 {

Fourier Series in Orthogonal Polynomials

Author : Boris Osilenker
Publisher : World Scientific
ISBN 13 : 9789810237875
Total Pages : 304 pages
Book Rating : 4.2/5 (378 download)

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Book Synopsis Fourier Series in Orthogonal Polynomials by : Boris Osilenker

Download or read book Fourier Series in Orthogonal Polynomials written by Boris Osilenker and published by World Scientific. This book was released on 1999 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Wavelets and Other Orthogonal Systems with Applications

Author : Gilbert G. Walter
Publisher : CRC Press
ISBN 13 : 9780849378782
Total Pages : 264 pages
Book Rating : 4.3/5 (787 download)

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Book Synopsis Wavelets and Other Orthogonal Systems with Applications by : Gilbert G. Walter

Download or read book Wavelets and Other Orthogonal Systems with Applications written by Gilbert G. Walter and published by CRC Press. This book was released on 1994-07-13 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Orthogonal Functions

Author : Giovanni Sansone
Publisher :
ISBN 13 :
Total Pages : 440 pages
Book Rating : 4.:/5 (3 download)

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Book Synopsis Orthogonal Functions by : Giovanni Sansone

Download or read book Orthogonal Functions written by Giovanni Sansone and published by . This book was released on 1959 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Fourier series with respect to general orthogonal systems

Author : A. M. Olevskij
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (77 download)

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Book Synopsis Fourier series with respect to general orthogonal systems by : A. M. Olevskij

Download or read book Fourier series with respect to general orthogonal systems written by A. M. Olevskij and published by . This book was released on 1975 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

An Introduction to Fourier Analysis

Author : Russell L. Herman
Publisher : CRC Press
ISBN 13 : 1498773729
Total Pages : 527 pages
Book Rating : 4.4/5 (987 download)

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Book Synopsis An Introduction to Fourier Analysis by : Russell L. Herman

Download or read book An Introduction to Fourier Analysis written by Russell L. Herman and published by CRC Press. This book was released on 2016-09-19 with total page 527 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book helps students explore Fourier analysis and its related topics, helping them appreciate why it pervades many fields of mathematics, science, and engineering. This introductory textbook was written with mathematics, science, and engineering students with a background in calculus and basic linear algebra in mind. It can be used as a textbook for undergraduate courses in Fourier analysis or applied mathematics, which cover Fourier series, orthogonal functions, Fourier and Laplace transforms, and an introduction to complex variables. These topics are tied together by the application of the spectral analysis of analog and discrete signals, and provide an introduction to the discrete Fourier transform. A number of examples and exercises are provided including implementations of Maple, MATLAB, and Python for computing series expansions and transforms. After reading this book, students will be familiar with: • Convergence and summation of infinite series • Representation of functions by infinite series • Trigonometric and Generalized Fourier series • Legendre, Bessel, gamma, and delta functions • Complex numbers and functions • Analytic functions and integration in the complex plane • Fourier and Laplace transforms. • The relationship between analog and digital signals Dr. Russell L. Herman is a professor of Mathematics and Professor of Physics at the University of North Carolina Wilmington. A recipient of several teaching awards, he has taught introductory through graduate courses in several areas including applied mathematics, partial differential equations, mathematical physics, quantum theory, optics, cosmology, and general relativity. His research interests include topics in nonlinear wave equations, soliton perturbation theory, fluid dynamics, relativity, chaos and dynamical systems.

An Introduction to Lebesgue Integration and Fourier Series

Author : Howard J. Wilcox
Publisher : Courier Corporation
ISBN 13 : 0486137473
Total Pages : 194 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis An Introduction to Lebesgue Integration and Fourier Series by : Howard J. Wilcox

Download or read book An Introduction to Lebesgue Integration and Fourier Series written by Howard J. Wilcox and published by Courier Corporation. This book was released on 2012-04-30 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Fourier Series

Author : Georgi P. Tolstov
Publisher : Courier Corporation
ISBN 13 : 0486141748
Total Pages : 354 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Fourier Series by : Georgi P. Tolstov

Download or read book Fourier Series written by Georgi P. Tolstov and published by Courier Corporation. This book was released on 2012-03-14 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Wavelets and Other Orthogonal Systems

Author : Gilbert G. Walter
Publisher : CRC Press
ISBN 13 : 1482285800
Total Pages : 391 pages
Book Rating : 4.4/5 (822 download)

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Book Synopsis Wavelets and Other Orthogonal Systems by : Gilbert G. Walter

Download or read book Wavelets and Other Orthogonal Systems written by Gilbert G. Walter and published by CRC Press. This book was released on 2018-10-03 with total page 391 pages. Available in PDF, EPUB and Kindle. Book excerpt: A bestseller in its first edition, Wavelets and Other Orthogonal Systems: Second Edition has been fully updated to reflect the recent growth and development of this field, especially in the area of multiwavelets. The authors have incorporated more examples and numerous illustrations to help clarify concepts. They have also added a considerable amount of new material, including sections addressing impulse trains, an alternate approach to periodic wavelets, and positive wavelet s. Other new discussions include irregular sampling in wavelet subspaces, hybrid wavelet sampling, interpolating multiwavelets, and several new statistics topics. With cutting-edge applications in data compression, image analysis, numerical analysis, and acoustics wavelets remain at the forefront of current research. Wavelets and Other Orthogonal Systems maintains its mathematical perspective in presenting wavelets in the same setting as other orthogonal systems, thus allowing their advantages and disadvantages to be seen more directly. Now even more student friendly, the second edition forms an outstanding text not only for graduate students in mathematics, but also for those interested in scientific and engineering applications.

An Introduction to Basic Fourier Series

Author : Sergei Suslov
Publisher : Springer Science & Business Media
ISBN 13 : 1475737319
Total Pages : 379 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis An Introduction to Basic Fourier Series by : Sergei Suslov

Download or read book An Introduction to Basic Fourier Series written by Sergei Suslov and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 379 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Orthogonal Transforms for Digital Signal Processing

Author : N. Ahmed
Publisher : Springer Science & Business Media
ISBN 13 : 364245450X
Total Pages : 274 pages
Book Rating : 4.6/5 (424 download)

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Book Synopsis Orthogonal Transforms for Digital Signal Processing by : N. Ahmed

Download or read book Orthogonal Transforms for Digital Signal Processing written by N. Ahmed and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended for those wishing to acquire a working knowledge of orthogonal transforms in the area of digital signal processing. The authors hope that their introduction will enhance the opportunities for interdiscipli nary work in this field. The book consists of ten chapters. The first seven chapters are devoted to the study of the background, motivation and development of orthogonal transforms, the prerequisites for which are a basic knowledge of Fourier series transform (e.g., via a course in differential equations) and matrix al gebra. The last three chapters are relatively specialized in that they are di rected toward certain applications of orthogonal transforms in digital signal processing. As such, a knowlegde of discrete probability theory is an essential additional prerequisite. A basic knowledge of communication theory would be helpful, although not essential. Much of the material presented here has evolved from graduate level courses offered by the Departments of Electrical Engineering at Kansas State University and the University of Texas at Arlington, during the past five years. With advanced graduate students, all the material was covered in one semester. In the case of first year graduate students, the material in the first seven chapters was covered in one semester. This was followed by a prob lems project-oriented course directed toward specific applications, using the material in the last three chapters as a basis.

A First Course in Wavelets with Fourier Analysis

Author : Albert Boggess
Publisher : John Wiley & Sons
ISBN 13 : 1118211154
Total Pages : 248 pages
Book Rating : 4.1/5 (182 download)

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Book Synopsis A First Course in Wavelets with Fourier Analysis by : Albert Boggess

Download or read book A First Course in Wavelets with Fourier Analysis written by Albert Boggess and published by John Wiley & Sons. This book was released on 2011-09-20 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive, self-contained treatment of Fourier analysis and wavelets—now in a new edition Through expansive coverage and easy-to-follow explanations, A First Course in Wavelets with Fourier Analysis, Second Edition provides a self-contained mathematical treatment of Fourier analysis and wavelets, while uniquely presenting signal analysis applications and problems. Essential and fundamental ideas are presented in an effort to make the book accessible to a broad audience, and, in addition, their applications to signal processing are kept at an elementary level. The book begins with an introduction to vector spaces, inner product spaces, and other preliminary topics in analysis. Subsequent chapters feature: The development of a Fourier series, Fourier transform, and discrete Fourier analysis Improved sections devoted to continuous wavelets and two-dimensional wavelets The analysis of Haar, Shannon, and linear spline wavelets The general theory of multi-resolution analysis Updated MATLAB code and expanded applications to signal processing The construction, smoothness, and computation of Daubechies' wavelets Advanced topics such as wavelets in higher dimensions, decomposition and reconstruction, and wavelet transform Applications to signal processing are provided throughout the book, most involving the filtering and compression of signals from audio or video. Some of these applications are presented first in the context of Fourier analysis and are later explored in the chapters on wavelets. New exercises introduce additional applications, and complete proofs accompany the discussion of each presented theory. Extensive appendices outline more advanced proofs and partial solutions to exercises as well as updated MATLAB routines that supplement the presented examples. A First Course in Wavelets with Fourier Analysis, Second Edition is an excellent book for courses in mathematics and engineering at the upper-undergraduate and graduate levels. It is also a valuable resource for mathematicians, signal processing engineers, and scientists who wish to learn about wavelet theory and Fourier analysis on an elementary level.

Ordinary and Partial Differential Equations

Author : Ravi P. Agarwal
Publisher : Springer Science & Business Media
ISBN 13 : 0387791469
Total Pages : 422 pages
Book Rating : 4.3/5 (877 download)

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Book Synopsis Ordinary and Partial Differential Equations by : Ravi P. Agarwal

Download or read book Ordinary and Partial Differential Equations written by Ravi P. Agarwal and published by Springer Science & Business Media. This book was released on 2008-11-13 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this undergraduate/graduate textbook, the authors introduce ODEs and PDEs through 50 class-tested lectures. Mathematical concepts are explained with clarity and rigor, using fully worked-out examples and helpful illustrations. Exercises are provided at the end of each chapter for practice. The treatment of ODEs is developed in conjunction with PDEs and is aimed mainly towards applications. The book covers important applications-oriented topics such as solutions of ODEs in form of power series, special functions, Bessel functions, hypergeometric functions, orthogonal functions and polynomials, Legendre, Chebyshev, Hermite, and Laguerre polynomials, theory of Fourier series. Undergraduate and graduate students in mathematics, physics and engineering will benefit from this book. The book assumes familiarity with calculus.