An index theorem for quotients of Bergman spaces on egg domains

TL;DR

This paper proves a $K$-homology index theorem for Toeplitz operators on Bergman spaces over egg domains, extending previous results from the unit ball to more general egg-like domains.

Contribution

The paper generalizes a $K$-homology index theorem for Toeplitz operators from the unit ball to a broader class of egg-like domains.

Findings

Established a $K$-homology index theorem for egg domains.

Extended previous results from the unit ball to egg domains.

Provided a framework for analyzing Toeplitz operators on complex domains.

Abstract

In this paper we prove a $K$-homology index theorem for the Toeplitz operators obtained from the multishifts of the Bergman space on several classes of egg-like domains. This generalizes our theorem with Douglas and Yu on the unit ball.