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

By Sergei Suslov

It used to be with the book of Norbert Wiener's publication ''The Fourier In­ tegral and sure of Its functions" [165] in 1933 by way of Cambridge Univer­ sity Press that the mathematical group got here to achieve that there's another method of the examine of c1assical Fourier research, specifically, throughout the idea of c1assical orthogonal polynomials. Little might he comprehend at the moment that this little thought of his might support bring in a brand new and exiting department of c1assical research referred to as q-Fourier research. makes an attempt at discovering q-analogs of Fourier and different comparable transforms have been made through different authors, however it took the mathematical perception and instincts of none different then Richard Askey, the grand grasp of certain services and Orthogonal Polynomials, to work out the usual connection among orthogonal polynomials and a scientific conception 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 remodel for a q-Harmonic Oscillator" [13], was once most likely the 1st major booklet during this zone. 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 vital element of the q-Fourier research, that merits thorough research, is the speculation of q-Fourier series.

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