Journal of Siberian Federal University. Mathematics & Physics / An Explicit Carleman Formula for the Dolbeault Cohomology

Full text (.pdf)
Issue
Journal of Siberian Federal University. Mathematics & Physics. 2010 3 (4)
Authors
Tarkhanov, Nikolai
Contact information
Tarkhanov, Nikolai : Institute of Mathematics, University of Potsdam , Am Neuen Palais, 10, Potsdam, 14469 Germany , e-mail:
Keywords
d-operator; cohomology; integral formulas
Abstract

We study formulas which recover a Dolbeault cohomology class in a domain of Cn through its values on an open part of the boundary. These are called Carleman formulas after the mathematician who first used such a formula for a simple problem of analytic continuation. For functions of several complex variables our approach gives the simplest formula of analytic continuation from a part of the boundary. The extension problem for the Dolbeault cohomology proves surprisingly to be stable at positive steps if the data are given on a concave piece of the boundary. In this case we construct an explicit extension formula.

Pages
450-460
Paper at repository of SibFU
https://elib.sfu-kras.ru/handle/2311/1834