Differentiation of functions on Vilenkin groups
by
Medo Pepić
Department of Mathematics, University of Sarajevo

In this paper we will consider a concept of differentiation of complex functions defined on Vilenkin groups, looking from the aspect of summability of Vilenkin series. In that sense we give matrix interpretation of C. N. Onneweer's concept of differentiation and then our generalization of that concept. We also give main properties of this generalized derivative. Moreover, we show that every method of summation of Vilenkin series, in a certain way, defines some concept of differentiation of integrable functions on Vilenkin groups.

Date received: April 20, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caex-62.