Subcoordinate representation of $p$-adic functions and generalization of Hensel's lemma
Izvestiya. Mathematics , Tome 82 (2018) no. 3, pp. 632-645
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In this paper we describe a new representation of $p$-adic functions,
the so-called subcoordinate representation. The main feature of
the subcoordinate representation of a $p$-adic function is that the values
of the function $f$ are given in the canonical form of the representation
of $p$-adic numbers. The function $f$ itself is determined by a tuple
of $p$-valued functions from the set $\{0,1,\dots,p-1\}$ into itself and
by the order in which these functions are used to determine the values of $f$.
We also give formulae that enable one to pass from the subcoordinate
representation of a $1$-Lipschitz function to its van der Put series
representation. The effective use of the subcoordinate
representation of $p$-adic functions is illustrated
by a study of the feasibility of generalizing Hensel's lemma.
Keywords:
$p$-adic numbers, Lipschitz functions, coordinate representation, van der Put series.
@article{IM2_2018_82_3_a9,
author = {E. I. Yurova Axelsson and A. Yu. Khrennikov},
title = {Subcoordinate representation of $p$-adic functions and generalization of {Hensel's} lemma},
journal = {Izvestiya. Mathematics },
pages = {632--645},
publisher = {mathdoc},
volume = {82},
number = {3},
year = {2018},
language = {en},
url = {http://geodesic.mathdoc.fr/item/IM2_2018_82_3_a9/}
}
TY - JOUR AU - E. I. Yurova Axelsson AU - A. Yu. Khrennikov TI - Subcoordinate representation of $p$-adic functions and generalization of Hensel's lemma JO - Izvestiya. Mathematics PY - 2018 SP - 632 EP - 645 VL - 82 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/IM2_2018_82_3_a9/ LA - en ID - IM2_2018_82_3_a9 ER -
%0 Journal Article %A E. I. Yurova Axelsson %A A. Yu. Khrennikov %T Subcoordinate representation of $p$-adic functions and generalization of Hensel's lemma %J Izvestiya. Mathematics %D 2018 %P 632-645 %V 82 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/item/IM2_2018_82_3_a9/ %G en %F IM2_2018_82_3_a9
E. I. Yurova Axelsson; A. Yu. Khrennikov. Subcoordinate representation of $p$-adic functions and generalization of Hensel's lemma. Izvestiya. Mathematics , Tome 82 (2018) no. 3, pp. 632-645. http://geodesic.mathdoc.fr/item/IM2_2018_82_3_a9/