Two Theorems on the Differentiation of Regular Convolution Quotients

We shall discuss two theorems on the derivatives of generalized functions. The class of generalized functions defined below as regular convolution quotients is a generalization of distributions and is also a generalization of the regular Mikusiński operators. Moreover, is a subclass of the quotients defined by J. and P. Mikusiński (Quotients de suites et leurs applications dans l’analyse fonctionnelle, Comptes Rendus, 239, série I (1981)). It is a subclass with some local properties, and we discuss some of these local properties. This subclass has been investigated by Piotr Mikusiński (Convergence of Boehmians, Japan. J. Math., Vol 9 (1983) and Boehmians as generalized functions, to appear Japan. J. Math.).