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- W1970847503 abstract "We prove a version of Montel?s Theorem for the case of continuous functions defined over the field Qp of p-adic numbers. In particular, we prove that, if ?m+1 h0 f (x) = 0 for all x ? Qp, and h0 satisfies |h0|p = p?N0, then, for all x0 ? Qp, the restriction of f over the set x0 + pN0Zp coincides with a polynomial px0 (x) = a0(x0) + a1(x0)x +...+ am(x0)xm. Motivated by this result, we compute the general solution of the functional equation with restrictions given by ?m+1 h f (x) = 0 (x ? X and h ? BX(r) = {x ? X : ?x? ? r}), whenever f : X ? Y, X is an ultrametric normed space over a non-Archimedean valued field (K, |?|) of characteristic zero, and Y is a Q-vector space. By obvious reasons, we call these functions uniformly locally polynomial." @default.
- W1970847503 created "2016-06-24" @default.
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- W1970847503 date "2014-01-01" @default.
- W1970847503 modified "2023-09-25" @default.
- W1970847503 title "A p-adic Montel Theorem and locally polynomial functions" @default.
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- W1970847503 doi "https://doi.org/10.2298/fil1401159a" @default.
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