Functional Analysis

Download PDF by Sergei Suslov: An Introduction to Basic Fourier Series (Developments in

By Sergei Suslov

ISBN-10: 1402012217

ISBN-13: 9781402012211

ISBN-10: 1441952446

ISBN-13: 9781441952448

It used to be with the e-book of Norbert Wiener's booklet ''The Fourier In­ tegral and likely of Its functions" [165] in 1933 by means of Cambridge Univer­ sity Press that the mathematical group got here to gain that there's an alternate method of the learn of c1assical Fourier research, particularly, in the course of the conception of c1assical orthogonal polynomials. Little may he be aware of at the moment that this little proposal 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 via different authors, however it took the mathematical perception and instincts of none different then Richard Askey, the grand grasp of particular capabilities and Orthogonal Polynomials, to determine the ordinary connection among orthogonal polynomials and a scientific idea of q-Fourier research. The paper that he wrote in 1993 with N. M. Atakishiyev and S. ok Suslov, entitled "An Analog of the Fourier remodel for a q-Harmonic Oscillator" [13], was once most likely the 1st major book during this quarter. 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 aspect of the q-Fourier research, that merits thorough research, is the idea of q-Fourier series.

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


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