Jiří Veselý

Mean Value Property and Harmonic Functions

The present state as well as the historical development of problems related to the mean value property of harmonic and caloric functions are discussed. The article is based on contributions of the authors at the meeting; it is a substantially extended update of [Net2].

Martin Compactification for Discrete Potential Theory and the Mean Value Property

A converse of the well-known theorem on themean value property of harmonic functions is given. It is shown that a positive measurable function is harmonic if it possesses arestricted mean value property. Earlier proofs obtained using the probabilistic techniques were given by Veech, Heath and Baxter. Our approach is based on a Martin type compactification built up with the help of some quite elementarya priori inequalities foraveraging kernels.

Potential theory--ICPT 94 : proceedings of the International Conference on Potential Theory, held in Kouty, Czech Republic, August 13-20, 1994

The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.

Some Remarks on Dirichlet Problem

In the theory of harmonic spaces (see [1], [3]) the Laplace and the heat equations can be investigated simultaneously. We shall do some remarks on boundary value problems from this abstract point of view.