%0 Journal Article
%T Fourier and Beyond: Invariance Properties of a Family of Integral Transforms
%A Cameron L. Williams
%A Bernhard G. Bodmann
%A Donald J. Kouri
%J Mathematics
%D 2014
%I arXiv
%X This paper presents a family of transforms which share many properties with the Fourier transform. We prove that these transforms are isometries on $L^2(\mathbb{R})$ and have the same scaling property. The transforms can be chosen to leave Gaussian-like functions invariant. We also establish short-time analogs of these transforms.
%U http://arxiv.org/abs/1403.4168v3