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arXiv · 2506.13117

Difference-differential fields of continuous functions

Seiji Nishioka
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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.

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Seiji Nishioka. 2025-06-16. Difference-differential fields of continuous functions. https://doi.org/10.1007/s00010-026-01276-8

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