M. Ya. Mazalov, “The Dirichlet problem for polyanalytic functions”, Mat. Sb., 2009, Volume 200, Number 10,Pages <nobr>59

This article is cited in 13 papers

The Dirichlet problem for polyanalytic functions

M. Ya. Mazalov

Military Academy of Air Defence Forces of Russia Federation named after A. M. Vasilevskii

Abstract: Connections between the boundary behaviour of polyanalytic functions and the structure of the boundary are investigated. In particular, a Jordan domain with Lipschitz boundary is constructed which is regular for the Dirichlet problem in the class of bianalytic functions.
Bibliography: 14 titles.

Keywords: polyanalytic functions, boundary properties, Luzin-Privalov construction, univalent functions, lacunary series, Rudin-Carleson theorem.

UDC: 517.538.5+517.956.2

MSC: 30D60

Received: 03.02.2009

DOI: 10.4213/sm7533