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

By Sergei Suslov

It was once with the ebook of Norbert Wiener's publication ''The Fourier In­ tegral and likely of Its functions" [165] in 1933 by way of Cambridge Univer­ sity Press that the mathematical neighborhood got here to gain that there's an alternate method of the examine of c1assical Fourier research, specifically, during the conception of c1assical orthogonal polynomials. Little might he be aware of at the moment that this little notion of his might support herald 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 common 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. ok Suslov, entitled "An Analog of the Fourier remodel for a q-Harmonic Oscillator" [13], used to be most likely the 1st major book 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 essential 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 speculation of q-Fourier series.

Show description

Read or Download An Introduction to Basic Fourier Series (Developments in Mathematics) PDF

Best functional analysis books

Exponentially Dichotomous Operators and Applications: 182 (Operator Theory: Advances and Applications)

During this monograph the common evolution operators of self sufficient first-order differential equations with exponential dichotomy on an arbitrary Banach house are studied intimately. Characterizations of those so-called exponentially dichotomous operators by way of their resolvents and additive and multiplicative perturbation effects are given.

Fundamental Solutions of Linear Partial Differential Operators: Theory and Practice

This monograph presents the theoretical foundations wanted for the development of basic suggestions and basic matrices of (systems of) linear partial differential equations. Many illustrative examples additionally exhibit strategies for locating such recommendations by way of integrals. specific realization is given to constructing the basics of distribution idea, followed through calculations of basic recommendations.

An Introduction to Frames and Riesz Bases (Applied and Numerical Harmonic Analysis)

This revised and elevated monograph provides the final conception for frames and Riesz bases in Hilbert areas in addition to its concrete realizations inside of Gabor research, wavelet research, and generalized shift-invariant platforms.  Compared with the 1st variation, extra emphasis is wear specific buildings with appealing houses.

Polyharmonic Boundary Value Problems: Positivity Preserving and Nonlinear Higher Order Elliptic Equations in Bounded Domains (Lecture Notes in Mathematics)

This obtainable monograph covers greater order linear and nonlinear elliptic boundary worth difficulties in bounded domain names, quite often with the biharmonic or poly-harmonic operator as best primary half. It offers quick entry to fresh effects and references.

Additional info for An Introduction to Basic Fourier Series (Developments in Mathematics)

Sample text

Download PDF sample

Rated 4.55 of 5 – based on 46 votes