JournalsprimsVol. 32 , No. 1DOI 10.2977/prims/1195163183

On the Solvability of Convolution Equations in Beurling's Distributions

  • Dae Hyeon Pahk

    Yonsei University, Seoul, South Korea
  • Byung Keun Sohn

    Inje University, Kimhae, South Korea
On the Solvability of Convolution Equations in Beurling's Distributions cover

Abstract

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 Sℰ'w, S * D'w = D'w is equivalent to the following: Every generalized distribution uℰ'w with S * uD'w is in Dw.