Fourier Series And Orthogonal Polynomials
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Fourier Series And Orthogonal Polynomials
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Author : Dunham Jackson
language : en
Publisher: Courier Corporation
Release Date : 2004-01-01
Fourier Series And Orthogonal Polynomials written by Dunham Jackson and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-01-01 with Mathematics categories.
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.
Fourier Series And Orthogonal Functions
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Author : Harry F. Davis
language : en
Publisher: Courier Corporation
Release Date : 2012-09-05
Fourier Series And Orthogonal Functions written by Harry F. Davis and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-09-05 with Mathematics categories.
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
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Author : Dunham Jackson
language : en
Publisher: American Mathematical Soc.
Release Date : 1941-12-31
Fourier Series And Orthogonal Polynomials written by Dunham Jackson and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1941-12-31 with Fourier series categories.
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 In Orthogonal Polynomials
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Author : Boris Osilenker
language : en
Publisher: World Scientific
Release Date : 1999-04-01
Fourier Series In Orthogonal Polynomials written by Boris Osilenker and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-04-01 with Mathematics categories.
This book presents a systematic course on general orthogonal polynomials and Fourier 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 L2μ; 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, mechanicians and physicists) whose work involves function theory, functional analysis, harmonic analysis and approximation theory.
Fourier Series And Orthogonal Polynomials
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Author : Dunham Jackson
language : en
Publisher:
Release Date : 2013-09
Fourier Series And Orthogonal Polynomials written by Dunham Jackson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-09 with categories.
Applications And Computation Of Orthogonal Polynomials
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Author : Walter Gautschi
language : en
Publisher: Springer Science & Business Media
Release Date : 1999-07-01
Applications And Computation Of Orthogonal Polynomials written by Walter Gautschi and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-07-01 with Mathematics categories.
This volume contains a collection of papers dealing with applications of orthogonal polynomials and methods for their computation, of interest to a wide audience of numerical analysts, engineers, and scientists. The applications address problems in applied mathematics as well as problems in engineering and the sciences.
Orthogonal Rational Functions
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Author : Adhemar Bultheel
language : en
Publisher: Cambridge University Press
Release Date : 1999-02-13
Orthogonal Rational Functions written by Adhemar Bultheel and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-02-13 with Mathematics categories.
This book generalises the classical theory of orthogonal polynomials on the complex unit circle, or on the real line to orthogonal rational functions whose poles are among a prescribed set of complex numbers. The first part treats the case where these poles are all outside the unit disk or in the lower half plane. Classical topics such as recurrence relations, numerical quadrature, interpolation properties, Favard theorems, convergence, asymptotics, and moment problems are generalised and treated in detail. The same topics are discussed for the different situation where the poles are located on the unit circle or on the extended real line. In the last chapter, several applications are mentioned including linear prediction, Pisarenko modelling, lossless inverse scattering, and network synthesis. This theory has many applications in theoretical real and complex analysis, approximation theory, numerical analysis, system theory, and in electrical engineering.
The Classical Orthogonal Polynomials
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Author : Brian George Spencer Doman
language : en
Publisher: World Scientific Publishing Company
Release Date : 2015-09-18
The Classical Orthogonal Polynomials written by Brian George Spencer Doman and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-18 with Mathematics categories.
This book defines sets of orthogonal polynomials and derives a number of properties satisfied by any such set. It continues by describing the classical orthogonal polynomials and the additional properties they have. The first chapter defines the orthogonality condition for two functions. It then gives an iterative process to produce a set of polynomials which are orthogonal to one another and then describes a number of properties satisfied by any set of orthogonal polynomials. The classical orthogonal polynomials arise when the weight function in the orthogonality condition has a particular form. These polynomials have a further set of properties and in particular satisfy a second order differential equation. Each subsequent chapter investigates the properties of a particular polynomial set starting from its differential equation.
Orthogonal Polynomials In Two Variables
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Author : P.K. Suetin
language : en
Publisher: Routledge
Release Date : 2022-03-31
Orthogonal Polynomials In Two Variables written by P.K. Suetin and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-31 with Mathematics categories.
Presenting a comprehensive theory of orthogonal polynomials in two real variables and properties of Fourier series in these polynomials, this volume also gives cases of orthogonality over a region and on a contour. The text includes the classification of differential equations which admits orthogonal polynomials as eigenfunctions and several two-dimensional analogies of classical orthogonal polynomials.
Expansion In Fourier Series And Orthogonal Polynomials With Matlab
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Author : Mutari Hajara Ali
language : en
Publisher:
Release Date : 2017-04-04
Expansion In Fourier Series And Orthogonal Polynomials With Matlab written by Mutari Hajara Ali and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-04-04 with categories.