Proper holomorphic correspondences and the Szego kernel in C

Moohyun Lee, Purdue University

Abstract

Let $\Omega\sb1$ and $\Omega\sb2$ be bounded domains in $\doubc$ with real analytic boundaries. We prove that if f is a proper holomorphic correspondence between $\Omega\sb1$ and $\Omega\sb2$, then it extends holomorphically past the boundary. We give an elementary proof that the Szego and the Bergman transforms on the unit ball in $\doubc\sp{n}$ preserve functions that extend smoothly to B. We prove that for any bounded domain in $\doubc$ with connectivity bigger than or equal to three, its Szego kernel has double zeros. We define the Szego polynomial and prove that the Szego subvariety is irreducible if and only if the Szego polynomial is irreducible.

Degree

Ph.D.

Advisors

Bell, Purdue University.

Subject Area

Mathematics

COinS