Fourier characterizations of Pilipovi? spaces

摘要

Let f be a function or distribution on Rd. We characterize Pilipovic space in terms of certain estimates of the involved functions and suitable choices of their fractional Fourier transforms. For the analysis we derive a multi-dimensional version of Phragmen-Lindelof's theorem.(c) 2022 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).