Download e-book for kindle: An Introduction to Basic Fourier Series (Developments in by Sergei Suslov

By Sergei Suslov

ISBN-10: 1402012217

ISBN-13: 9781402012211

ISBN-10: 1441952446

ISBN-13: 9781441952448

It used to be with the ebook of Norbert Wiener's booklet ''The Fourier In­ tegral and sure of Its purposes" [165] in 1933 by way of Cambridge Univer­ sity Press that the mathematical neighborhood got here to achieve that there's another method of the learn of c1assical Fourier research, specifically, throughout the concept of c1assical orthogonal polynomials. Little may he comprehend at the moment that this little notion of his may support bring in a brand new and exiting department of c1assical research known as q-Fourier research. makes an attempt at discovering q-analogs of Fourier and different comparable transforms have been made by means of different authors, however it took the mathematical perception and instincts of none different then Richard Askey, the grand grasp of distinctive capabilities and Orthogonal Polynomials, to determine the average connection among orthogonal polynomials and a scientific thought of q-Fourier research. The paper that he wrote in 1993 with N. M. Atakishiyev and S. okay Suslov, entitled "An Analog of the Fourier rework for a q-Harmonic Oscillator" [13], was once most likely the 1st major booklet during this region. The Poisson k~rnel for the contin­ uous q-Hermite polynomials performs a task of the q-exponential functionality for the analog of the Fourier imperative less than considerationj see additionally [14] for an extension of the q-Fourier rework to the overall case of Askey-Wilson polynomials. (Another very important factor of the q-Fourier research, that merits thorough research, is the speculation of q-Fourier series.

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An Introduction to Basic Fourier Series (Developments in Mathematics) by Sergei Suslov

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