On the convolution in the space \({\mathcal D}^{\prime(M_ p)}_{L^ 2}\) (Q1114123)

The author introduced the space \({\mathcal D}_{{\mathcal L}^ 2}^{'(M_ p)}\) as a subspace of the space of Beurling ultradistributions [Rend. Math. Univ. Padova 77, 1-13 (1987; Zbl 0636.46043)]. The present paper is motivated by certain questions raised on the convolution in the space in the above mentioned paper. Finally conditions on a convolutor S for the solvability and the hypoellipticity of a convolution equation \(S\odot U=V\) in the same space are given. There is a misprint in the summary - the symbol * should be replaced by \(\odot\). Certain results obtained by the author in a forthcoming paper have been used in this paper [Boundary value representations of a class of Beurling ultradistributions, Port. Math., to appear].