Analytic Continuation in Classical Potential Theory
In this mini-course, we outline a modern approach to several classical questions in potential theory, e.g., uniqueness problem for polyharmonic functions, Szego's theorem on singularities of axially symmetric harmonic expansions, analytic continuation of gravitational potentials inside the regions occupied by masses and reflections principle for harmonic functions. Our point view will be based on the modern theory of singularities of solutions of linear holomorphic PDE in C^n, in particular, a saro version of the Cauchy-Kowalewski theorem, Zerner's theorem and the Bony-Schapira theorem. All the notions needed to develop the course will be carefully defined and illustrated by examples.