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

By Sergei Suslov

ISBN-10: 1402012217

ISBN-13: 9781402012211

ISBN-10: 1441952446

ISBN-13: 9781441952448

It used to be with the book of Norbert Wiener's ebook ''The Fourier In­ tegral and likely of Its functions" [165] in 1933 by way of Cambridge Univer­ sity Press that the mathematical group got here to gain that there's another method of the research of c1assical Fourier research, particularly, throughout the concept of c1assical orthogonal polynomials. Little may he recognize at the moment that this little inspiration of his may 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 via different authors, however it took the mathematical perception and instincts of none different then Richard Askey, the grand grasp of detailed features and Orthogonal Polynomials, to determine the normal 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. 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 zone. The Poisson k~rnel for the contin­ uous q-Hermite polynomials performs a job of the q-exponential functionality for the analog of the Fourier imperative lower than considerationj see additionally [14] for an extension of the q-Fourier remodel 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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An Introduction to Basic Fourier Series (Developments in Mathematics) by Sergei Suslov

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