Convolution equations in Beurling's distributions (Q1113058)

Solvability of convolution equations was investigated by \textit{L. Ehrenpreis} [Am. J. Math. 82, 522-588 (1960; Zbl 0098.084)] and \textit{L. Hörmander} [Ann. Math. 76, 148-170 (1962; Zbl 0109.085)] in the space of Schwartz's distributions. This paper discusses solvability of systems of convolution equations in Beurling's distributions [\textit{G. Björk}: Linear partial differential operators and generalized distributions, Ark. Math. 6, 351-407 (1966; Zbl 0166.365)]. The author maintains that his results in this paper extend some of Hörmander's. The elements of \({\mathcal D}_{\omega}\) are called Beurling test functions and the space of all continuous linear functionals on \({\mathcal D}_{\omega}\) is represented by \({\mathcal D}_{\omega}'\). By \({\mathcal D}^ m_{\omega}\) is denoted the product of m copies of \({\mathcal D}_{\omega}(R^ n)\). Some existence theorems in \({\mathcal D}_{\omega}'\) are given in section 2 and section 3 contains some existence theorems in \(D_{\omega}^{'m}\).