On the Solvability of Convolution Equations in Beurling's Distributions
Dae Hyeon PahkYonsei University, Seoul, South Korea
Byung Keun SohnInje University, Kimhae, South Korea
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