Title: A Heat Equation on some Adic Completions of Q and Ultrametric Analysis,
Abstract: This article deals with a Markov process related to the fundamental solution
of a heat equation on the direct product ring Q_S, where Q_S is a finite direct
product of p-adic fields. The techniques developed here are different from the
well known ones: they are geometrical and very simple. As a result, the
techniques developed here provides a general framework of these problems on
other related ultrametric groups.