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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.08547 |
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| _version_ | 1866915206167265280 |
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| author | Zubarev, Alexander P. |
| author_facet | Zubarev, Alexander P. |
| contents | It is shown that any continuous function depending on several $p$-adic variables, each of which is defined on $\mathbb{Z}_{p}$, can be represented as a superposition of continuous functions of one $p$-adic variable. This statement is true for both functions with values in $\mathbb{R}$ and functions with values in $\mathbb{Q}_{p}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_08547 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the analog of the Kolmogorov-Arnold superposition representation for continuous functions of several $p$-adic variables Zubarev, Alexander P. Mathematical Physics Number Theory It is shown that any continuous function depending on several $p$-adic variables, each of which is defined on $\mathbb{Z}_{p}$, can be represented as a superposition of continuous functions of one $p$-adic variable. This statement is true for both functions with values in $\mathbb{R}$ and functions with values in $\mathbb{Q}_{p}$. |
| title | On the analog of the Kolmogorov-Arnold superposition representation for continuous functions of several $p$-adic variables |
| topic | Mathematical Physics Number Theory |
| url | https://arxiv.org/abs/2503.08547 |