Demonstrates a new transforming operator in complex-valued continuous functions, highlighting its implications on difference fields.
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 ) .
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Seiji Nishioka (2026) studied this question.
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