1988 | OriginalPaper | Chapter
Two Theorems on the Differentiation of Regular Convolution Quotients
Author : Thomas K. Boehme
Published in: Generalized Functions, Convergence Structures, and Their Applications
Publisher: Springer US
Included in: Professional Book Archive
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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.).