Irina Markina - Microlocal and Global Analysis,...
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Irina Markina - Microlocal and Global Analysis, Interactions with Geometry
On Cauchy-Szegö kernel for quaternionic Siegel upper half space.
In the talk we introduce a quaternionic analogue of the Heisenberg group and explain the relation
between this group and the quaternionic analogous of the Siegel upper half space. We discuss regular functions,
that are counterpart of complex holomorphic functions for quaternionic setting. The Hardy space is the space of
regular functions in the Siegel upper half space with L2 boundary values. We construct the Cauchy-Szego kernel
for the Cauchy-Szego projection integral operator from the space of L2-integrable functions dened on the boundary
of the quaternionic Siegel upper half space to the space of boundary values of the quaternionic regular functions
of the Hardy space over the quaternionic Siegel upper half space. We also present the fundamental solution for a
hypoelliptic operator related to the boundary of the Siegel upper half space. The talk is based on the joint work with
Der Chen Chang (Georgetown U