Difference-differential fields of continuous functions
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866914383429369856 |
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| author | Nishioka, Seiji |
| author_facet | Nishioka, Seiji |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_13117 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Difference-differential fields of continuous functions Nishioka, Seiji Commutative Algebra 12H10, 12H05, 39A05 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. |
| title | Difference-differential fields of continuous functions |
| topic | Commutative Algebra 12H10, 12H05, 39A05 |
| url | https://arxiv.org/abs/2506.13117 |