%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