Get An Introduction to Basic Fourier Series (Developments in PDF

Functional Analysis

By Sergei Suslov

It used to be with the e-book of Norbert Wiener's publication ''The Fourier In­ tegral and likely of Its functions" [165] in 1933 by means of Cambridge Univer­ sity Press that the mathematical neighborhood got here to gain that there's an alternate method of the research of c1assical Fourier research, particularly, during the idea of c1assical orthogonal polynomials. Little might he be aware of at the moment that this little suggestion of his could support herald 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 way of different authors, however it took the mathematical perception and instincts of none different then Richard Askey, the grand grasp of exact services and Orthogonal Polynomials, to work out the traditional 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 rework for a q-Harmonic Oscillator" [13], used to be most likely the 1st major booklet during this sector. 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 critical below considerationj see additionally [14] for an extension of the q-Fourier rework to the overall case of Askey-Wilson polynomials. (Another vital component 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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