Functional transformations

All mathematical terms used in this article are defined in the articles Functional analysis [A 101] , Complex analysis and Harmonic analysis, distributions, convolution in the treatise Fundamental Sciences.

To assist the reader, we have often briefly explained the meaning of the term used, in brackets after the term. As the subject of functional transformations is extremely vast, we have chosen to present only a few of them – the most commonly used – and to give a very limited number of applications, without presenting the physical problems and their modeling –. For this, we refer to the bibliographical references indicated and in particular to .

Our aim here is to quickly present efficient tools for systematically solving a wide range of problems of very different origins, and in particular partial differential equation problems in natural functional frameworks for modeling the physical problem posed.

This article naturally has partial overlaps with the Harmonic analysis, distributions and convolution articles. , Hypergeometric functions. Bessel functions and Eulerian functions. Classical orthogonal polynomials .