Solution of boundary-value problems in the theory of analytic functions of several variables in Vladimirov algebras

Abstract

A solution is given for the Riemann problem for tubular domains in Vladimirov algebras in closed form by means of an integral representation of Bochner-Vladimirov type which is constructed here. In particular, the Schwartz problem is solved. The statement of the Hilbert problem in Vladimirov algebras is examined and its solution is given by a reduction to the Riemann problem, and in one case by a reduction to the Schwartz problem.