Entire and Meromorphic Functions in Several Complex Variables

Florida International University, Miami FL

Investigators

Abstract

The proposed research is directed at topics in several complex variables on entire holomorphic maps, interpolation problems, and value distribution theory. The principle investigator proposes to continue his study on the well-known transcendental Bezout problem about the growth of the volume of entire analytic sets and find sharp estimates on the counting functions of zeros of entire holomorphic maps. He also proposes to study interpolation problems for weighted spaces of entire functions, one of fundamental and central problems in several complex variables. In particular, he wishes to characterize interpolating varieties geometrically, which is closely tied with his study on the Bezout problem. In the third direction, he would like to continue his research on value distribution theory with a special attention given to the refined Nevanlinna second fundamental theorem for slowly moving targets and its relations to other problems such as uniqueness problems of meromorphic functions and meromorphic solutions of partial differential equations. The above problems are important not just from the point of view of several complex variables, but also from their relations and applications to other subjects such as harmonic analysis, transcendental number theory, systems theory and engineering. For instance, many important problems like finding and representing solutions to partial differential equations or systems of convolution equations arising in signal processing, image compression, materials testing, etc. are equivalent to interpolation problems for entire functions in weighted spaces. The proposed research aims at developing and advancing both theories and applications for the above areas in several complex variables.