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Fourier series with respect to general orthogonal systems

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Published by Springer-Verlag in Berlin, New York .
Written in English


  • Functions, Orthogonal.,
  • Series, Orthogonal.,
  • Fourier series.

Book details:

Edition Notes

StatementA. M. Olevskiĭ ; translated from the Russian by B. P. Marshall and H. J. Christoffers.
SeriesErgebnisse der Mathematik und ihrer Grenzgebiete ;, Bd. 86
LC ClassificationsQA404.5 .O4313
The Physical Object
Paginationviii, 136 p. ;
Number of Pages136
ID Numbers
Open LibraryOL5065809M
ISBN 100387071032
LC Control Number74032297

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Note: Citations are based on reference standards. However, formatting rules can vary widely between applications and fields of interest or study. The specific requirements or preferences of your reviewing publisher, classroom teacher, institution or organization should be applied. Oct 11,  · The text treats expansions in Fourier series, general orthogonal expansions, convergence of Fourier series, operations with Fourier series, double Fourier series, Fourier integrals and transforms, Bessel functions and Fourier-Bessel series, the eigenfunction method and its use in solving boundary value problems of mathematical analysis Cited by: Fourier Series pdf. This note covers the following topics: Computing Fourier Series, Computing an Example, Notation, Extending the function, Fundamental Theorem, Musical Notes, Parseval's Identity, Periodically Forced ODE's, General Periodic Force, Gibbs Phenomenon. Richard A. Silverman's series of translations of outstanding Russian textbooks and monographs is well-known to people in the fields of mathematics, physics, and engineering. The present book is another excellent text from this series, a valuable addition to the English-language literature on Fourier series. This edition is organized into nine well-defined chapters: Trigonometric Fourier Series 3/5(3).

The active development of the theory of orthogonal series in the 20th century has been enhanced by the use of orthonormal systems of functions and series with respect to them in the most varied areas of science (mathematical physics, computational mathematics, functional analysis, quantum mechanics, mathematical statistics, operational calculus. Generalized Fourier Series. A generalized Fourier series is a series expansion of a function based on a system of orthogonal polynomials. By using this orthogonality, a piecewise continuous function \({f\left(x \right)}\) can be expressed in the form of generalized Fourier series expansion. Nov 15,  · Fourier Series with Respect to General Orthogonal Systems Paperback – Nov 15 by A. Olevskii (Author), B.P. Marshall (Translator), H.J. Christoffers (Translator) & See all 2 formats and editions Hide other formats and editions. Amazon Price New from Author: A. Olevskii. Fourier series with respect to general orthogonal systems. Berlin ; New York: Springer-Verlag. MLA Citation. Olevskii, A. M. Fourier series with respect to general orthogonal systems / A. M. Olevskii ; translated from the Russian by B. P. Marshall and H. J. Christoffers Springer-Verlag Berlin ; New York Australian/Harvard Citation.

Convergence of Fourier series with respect to general orthonormal systems. Authors; Authors and affiliations; L. D. Gogoladze; Orthogonal Series, Approximation Theory, and Related Questions, Collection of papers dedicated to the 60th anniversary of Academician B. S. Kashin (MAIK, Moscow, Cited by: 3. In mathematics, a Fourier series (/ ˈ f ʊr i eɪ,-i ər /) is a periodic function composed of harmonically related sinusoids, combined by a weighted appropriate weights, one cycle (or period) of the summation can be made to approximate an arbitrary function in that interval (or the entire function if it too is periodic).As such, the summation is a synthesis of another function. Chapt Orthogonal Functions and Fourier series J.-P. Gabardo [email protected] Orthogonal systems Fourier series on general intervals • The series expansion (4) in terms of the trigonometric system T is called the Fourier series expansion of f(x) on [−π,π]. Oct 31,  · Orthogonal Set of Functions (Fourier Series). Here I give the definition of an orthogonal set of functions and show a set of functions is an orthogonal set. The set I use is important as it.