On the distribution kernels of Toeplitz operators on CR manifolds

TL;DR

This paper derives a formula for the diagonal values of the second coefficient in the kernel expansion of Toeplitz operators on CR manifolds and establishes their asymptotic behavior under certain conditions.

Contribution

It provides a new explicit formula for the second coefficient of the kernel expansion and extends asymptotic expansion results to CR orbifolds.

Findings

Explicit formula for the second coefficient at the diagonal

Asymptotic expansions for Toeplitz operators on CR orbifolds

Extension of results to non-strictly pseudoconvex CR manifolds

Abstract

We study the distribution kernel of a Toeplitz operator associated with a classical pseudodifferential operator on a compact, embeddable, strictly pseudoconvex CR manifold. The main result consists of a formula for the values at the diagonal of the second coefficient in the expansion of the symbol of the kernel. We also establish asymptotic expansions for Toeplitz operators on the positive part of a compact not necessary strictly pseudoconvex CR orbifold under certain natural assumptions.