Operators in Complex Analysis Seminar

The Leray (or Cauchy-Leray) transform is a higher dimensional analogue of the familiar one variable Cauchy transform: It builds holomorphic functions on a domain from L^2 data given on the boundary of that domain. This talk will focus on the spectral theory of this transform on a family of hypersurfaces. Following an orthogonal decomposition of the space of L^2 boundary functions, detailed analysis of the operator on each subspace will be performed. This will take us deep into the realm of Gamma function asymptotics, and the celebrated Euler-Maclaurin formula will save the day. Speaker(s): Luke Edholm (University of Michigan)