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

By Sergei Suslov

It was once 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 neighborhood got here to achieve that there's another method of the learn of c1assical Fourier research, particularly, in the course of the thought of c1assical orthogonal polynomials. Little may he recognize at the moment that this little suggestion of his could aid 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 by means of different authors, however it took the mathematical perception and instincts of none different then Richard Askey, the grand grasp of exact capabilities 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 rework for a q-Harmonic Oscillator" [13], used to be most likely the 1st major ebook 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 quintessential lower than considerationj see additionally [14] for an extension of the q-Fourier remodel to the overall case of Askey-Wilson polynomials. (Another vital aspect of the q-Fourier research, that merits thorough research, is the speculation of q-Fourier series.

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