Invertibility of Toeplitz operators with polyanalytic symbols

Document Type: Original Article


University of Toledo, USA


‎For a class of continuous functions including complex polynomials in $z,\bar{z},$ 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 nontrivial operator theoretic results about such Toeplitz operators‎, ‎including a new criterion for invertibility of a Toeplitz operator for a class of harmonic symbols‎.


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