Hardy's Theorem for the (k,(2)/(n))-Fourier Transform

2025/03/03 by Jilani, Hanen, Negzaoui, Selma
#33C10 #35A22 #42A38 #44A15 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2503.01094

Abstract

By comparing a function and its (k, (2)/(n))-Fourier transform to a Gaussian analogue, e^{-na|x|^(2)/(n)}, we establish a Hardy-type uncertainty principle using Phragmén-Lindlöf lemma. Furthermore, we investigate the heat equation in this context, deriving a dynamical version of Hardy's theorem that illustrates the temporal evolution of the uncertainty principle. We also extend our results to L^p-L^q versions, proving Miyachi-type and Cowling-Price-type theorems for the (k,(2)/(n))-Fourier transform.

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