Analysis Seminar: Irina Markina

Speaker: Irina Markina, Professor, Mathematical Department, UiB.

 

Title: Definition of boundary complex and corresponding box operator.

Abstract: Last time we introduced Dolbeault complex and box operator on a complex manifold. We will use the same ideas to introduce the boundary box operator for C-R manifolds. After discussing general ideas we will make concrete calculations for the boundary of the Siegel upper half space, that is isomorphic to the Heisenberg group. We will calculate the boundary box operator in terms of left invariant vector fields of the Heisenberg group and discuss the fundamental solution for boundary box operator.