Fourier Transforms and Their Applications
Lokenath Debnath, Dambaru Bhatta · 2014
Joseph Fourier “The theory of Fourier series and integrals has always had major difficulties and necessitated a large mathematical apparatus in dealing with questions of convergence. It engendered the development of methods of summation, although these did not lead to a completely satisfactory solution of the problem. ... For the Fourier transform, the introduction of distributions (hence, the space S ) is inevitable either in an explicit or hidden form. ... As a result one may obtain all that is desired from the point of view of the continuity and inversion of the Fourier transform.”