Date

Speaker and Title

Aug 24

Wayne Eby, Temple University Moments and the Morera Problem on the Heisenberg Group Abstract: The standard Morera theorem allows us to conclude a function is analytic in a region if its integral vanishes over any simple closed curve in the region. The Morera problem looks at obtaining the same conclusions with a reduction in the integral conditions, for instance integrating only over circles of a fixed radius. It is interesting to investigate these same issues in regard to CR functions on the Heisenberg group. The results characterize when a function on the Heisenberg group is a CR function based on the vanishing of certain integrals taken along complex spheres embedded in the Heisenberg group. Another important aspect of these results is the role played by moment factors in the integrals. When the integrals include moments, it is possible to obtain conclusions involving monomials in the standard complex basis of left invariant vector fields on the Heisenberg group.