Difference-differential fields of continuous functions
Abstract
Abstract The set $$\mathcal {C}$$ C of complex-valued continuous functions on $$[0,\infty )$$ [ 0 , ∞ ) is a ring for addition and convolution. It has the quotient field $$Q(\mathcal {C})$$ Q ( C ) , by which J. Mikusiński developed his operational calculus. In this paper, we revisit a derivation and a transforming operator for $$Q(\mathcal {C})$$ 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 $$Q(\mathcal {C})$$ Q ( C ) .
Fields of Study & Subjects
Advanced Differential Equations and Dynamical Systems
advanced mathematical theories
Advanced Topology and Set Theory
Publication details
- Journal / source
- Aequationes Mathematicae
- Volume
- 100
- Issue
- 2
- Publication date
- 10 March 2026
- Language
- EN