Seminar

Radon phenomenon (the terminology is due to L. Ehrenpreis) addresses the situations when one can judge the properties of an object (a function or a manifold) from its restrictions to certain subsets (submanifolds, sections, slices...).

In context of PDEs, one wants to know whether a function is a solution
of a given PDE if it coincides with solutions of this PDE on a family of
submanifolds. In complex analysis, one deals with Cauchy-Riemann equation
and is led to a problem of characterization of holomorphic or CR functions
or, more generally, holomorphic or CR manifolds, or their boundaries, in
terms of zero complex moments on varieties of closed curves.

I will present a survey of results of this nature obtained in the last
decade for elliptic and Cauchy-Riemann equations. Problems of this type
arise, in particular, in integral geometry and tomography.