Buma L. Fridman

Properties of fixed point sets and a characterization of the ball in Cn

We study the fixed point sets of holomorphic self- maps of a bounded domain in C n . Specifically we investigate the least number of fixed points in general position in the domain that forces any automorphism (or endomorphism) to be the identity. We have discovered that in terms of this number one can give the necessary and sufficient condition for the domain to be biholomor- phic to the unit ball. Other theorems and examples generalize and complete previous results in this area, especially the recent work of Jean-Pierre Vigue.

PERTURBATION OF DOMAINS AND AUTOMORPHISM GROUPS

The paper is devoted to the description of changes of the structure of the holomorphic automorphism group of a bounded domain in C n under small perturbation of this domain in the Hausdorff metric. We consider a number of examples when an arbitrary small perturbation can lead to a domain with a larger group, present theorems concerning upper semicontinuity property of some invariants of automorphism groups. We also prove that the dimension of an abelian subgroup of the automorphism group of a bounded domain in C n does not exceed n.

Numerical Harmonic Analysis on the Hyperbolic Plane

Results are reported of a numerical implementation of the hypcrbolic Fourier transform and the geodesic and horocyclic Radon transforms on the hyperbolic plane, and of their inverses. The study is motivated by the hyperbolic geometry approach to the linearized inverse conductivity problem, suggested by C. A. Berenstein and E. Casadio Tarabusi.