Fredholm Toeplitz operators on doubling Fock spaces

TL;DR

This paper extends the characterization of Fredholm Toeplitz operators to doubling Fock spaces with subharmonic weights, involving complex geometric analysis due to the Bergman metric.

Contribution

It generalizes previous results by analyzing Fredholm properties on doubling Fock spaces with a more complex geometric structure.

Findings

Extended Fredholm characterization to doubling Fock spaces

Developed new geometric analysis techniques for Bergman metric

Identified conditions for Fredholmness in more general settings

Abstract

Recently the authors characterized the Fredholmn properties of Toeplitz operators on weighted Fock spaces when the Laplacian of the weight function is bounded below and above. In the present work the authors extend their characterization to doubling Fock spaces with a subharmonic weight whose Laplacian is a doubling measure. The geometry induced by the Bergman metric for doubling Fock spaces is much more complicated than that of the Euclidean metric used in all the previous cases to study Fredholmness, which leads to considerably more involved calculations.