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arXiv · 2503.08547

On the analog of the Kolmogorov-Arnold superposition representation for continuous functions of several $p$-adic variables

Alexander P. Zubarev
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Abstract

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 $\mathbb{Q}_{p}$.

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Alexander P. Zubarev. 2025-03-11. On the analog of the Kolmogorov-Arnold superposition representation for continuous functions of several $p$-adic variables. https://doi.org/10.1134/s2070046625030082

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