Solvability of Convolution Operators

Abstract

We study the Surjectivity of convolution operators on the spaces of hyperfunctions and Fourier hyperfunctions. On the space of hyperfunctions, we give a sufficient condition (the kernel is a nonzero ultradistribution), weaker than earlier conditions. On the space of Fourier hyperfunction, we give a new sufficient condition and new necessary conditions for the Surjectivity. Especially in one dimensional case, they become a sufficient and necessary condition. To this aim we use the Fourier analysis as in L. Ehrenpreis [E-2] and T. Kawai [Ka-1].