An Uncertainty Principle of Paley and Wiener on Euclidean Motion Group
Journal of Fourier Analysis and Applications
A classical result due to Paley and Wiener characterizes the existence of a non-zero function in L2(R) , supported on a half line, in terms of the decay of its Fourier transform. In this paper we prove an analogue of this result for compactly supported continuous functions on the Euclidean motion group M(n). We also relate this result to a unique continuation property of solutions to the initial value problem for time-dependent Schrödinger equation on M(n).
Bhowmik, Mithun and Sen, Suparna, "An Uncertainty Principle of Paley and Wiener on Euclidean Motion Group" (2017). Journal Articles. 2337.