The proposed research consists in developing topics for research in the area of function theory in one or several complex variables: a) exceptional sets. The aim is to describe by means of capacities or Haussdorf measures the sets of singularities, in a wide sense, of certain classes of holomorphic functions; b) stable rank in algebras of analytic functions. We would like to clarify the relation between this algebraic property and analytic properties; c) Sobolev spaces of holomorphic or invariantly harmonic functions. Here the project consists in developing in the context of several complex variables a parallel theory to the one in real analysis; d) Pompeiu and Morera problems. We would like to continue the study of these classical problems, in the frame of several complex variables.
|Effective start/end date||26/05/93 → 26/05/96|