Regularization of $p$-Adic Distributions Associated to Functions on $p$-Adic Fields With Moderate Variation

Year 2021, Volume: 9 Issue: 2, 74 - 80, 01.06.2021

Altan Erdoğan

https://doi.org/10.36753/mathenot.794789

Abstract

The $p$-adic distributions attached to ordinary functions defined on $p$-adic fields with moderate variation are studied. We first give a sufficient growth condition on ordinary functions to construct $p$-adic distributions. Then a moderate variation condition on functions for regularization of these $p$-adic distributions is imposed which provides a general method to construct $p$-adic measures. The $p$-adic integrals against these measures are also explicitly transformed to integrals against Bernoulli measures.

Keywords

p-adic analysis, p-adic integration, Bernoulli measures, p-adic Gamma measures

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