JournalsprimsVol. 32, No. 1pp. 157–162

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
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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 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. 157–162

DOI 10.2977/PRIMS/1195163183