Abstract The set C C of complex-valued continuous functions on [0, ) [ 0, ∞) is a ring for addition and convolution. It has the quotient field Q (C) Q (C), by which J. Mikusiński developed his operational calculus. In this paper, we revisit a derivation and a transforming operator for Q (C) Q (C) discussed in his textbook, and define a new transforming operator related to the q -shift operator, which gives structures of a q -difference field and a difference field of Mahler type to Q (C) Q (C).
Seiji Nishioka (Tue,) studied this question.