Multidimensional Short-Time Fractional Fourier Transform

Abstract

In this paper, we present a theoretical framework that defines and describes the fundamental aspects of the L-2(R-d) theory of multidimensional short-time fractional Fourier transform. We begin by defining multidimensional short-time fractional Fourier transform, before going on to describe its properties and the inner product relation. Later, we consider its d-dimensional and 2d-dimensional inverse transforms. Finally, we arrive at the sufficient conditions for the boundedness of the multidimensional short-time fractional Fourier transform acting on Lebesgue spaces.