Explicit Carleman formulas for the Dolbeault cohomology in concave domains

Ivan V. Shestakov

Institute of Mathematics, Siberian Federal University, Krasnoyarsk, Russia

Abstract: In 1999 M. Nacinovich et al. suggested an abstract method for constructing Carleman formulas for the Dolbeault complex. What has been lacking are simple and explicit examples. In this article we present a Carleman formula for Dolbeault cohomology classes given on a part of the boundary whose comlement is concave. As corollary we derive a uniqueness theorem for the Dolbeault cohomology.

Keywords: Carleman formula, Dolbeault cohomology, analytic continuation.

UDC: 517.55

Received: 11.01.2011
Received in revised form: 11.02.2011
Accepted: 10.04.2011