This article is cited in 3 papers

Construction of a set of $p$-adic distributions

U. A. Rozikov, Z. T. Tugyonov

Institute of Mathematics, Tashkent, Uzbekistan

Abstract: Adapting some methods for real-valued Gibbs measures on Cayley trees to the $p$-adic case, we construct several $p$-adic distributions on the set $\mathbb Z_p$ of $p$-adic integers. In addition, we give conditions under which these $p$-adic distributions become $p$-adic measures (i.e., bounded distributions).

Keywords: Cayley tree, $p$-adic number, $p$-adic distribution, $p$-adic measure.

Received: 09.12.2016

DOI: 10.4213/tmf9314

 English version: Theoretical and Mathematical Physics, 2017, 193:2, 1694–1702

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