A distributional approach to Namias' fractional Fourier transforms

Abstract

SynopsisA fractionalisation of the Fourier transform was developed formally by Namias. By workingin ℐ, we found that this theory could be made mathematically rigorous. Here we extend our previous results to the space ℐ′ to consider fractional powers of the distributional Fourier transform. The paper concludes with an application to an ordinary differential equation which shows how a distributional approach can sometimes be more useful than a classical approach.