Let D'w be the space of Beurling's generalized distributions on Rn and ℰ'w the spaces of generalized distributions which has compact support. We show that, for S ∈ ℰ'w, S * D'w = D'w is equivalent to the following: Every generalized distribution u ∈ ℰ'w with S * u ∈ D'w is in Dw.
Cite this article
Dae Hyeon Pahk, Byung Keun Sohn, On the Solvability of Convolution Equations in Beurling's Distributions. Publ. Res. Inst. Math. Sci. 32 (1996), no. 1, pp. 157–162DOI 10.2977/PRIMS/1195163183