Invertibility of Toeplitz operators with polyanalytic symbols
arXiv:1702.05772
Abstract
Given a polyanalytic function, we show that the corresponding Toeplitz operator on the Bergman space of the unit disc can be expressed as a quotient of certain differential operators with holomorphic coefficients. This enables us to obtain several operator theoretic results including a criterion for invertibility of a Toeplitz operator.
7 pages, revised version, all comments welcome