Difference-differential fields of continuous functions
Commutative Algebra
2026-03-12 v1
Abstract
The set C of complex-valued continuous functions on [0,\infty) is a ring by the addition and the convolution. It has the quotient field Q(C), by which J. Mikusinski developed his operational calculus. In this paper, we revisit a derivation and a transforming operator for Q(C) written in his textbook, and define another 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). Appropriate derivatives are also considered.
Cite
@article{arxiv.2506.13117,
title = {Difference-differential fields of continuous functions},
author = {Seiji Nishioka},
journal= {arXiv preprint arXiv:2506.13117},
year = {2026}
}