Tusi Mathematical Research Group (TMRG)Advances in Operator Theory2538-225X4420191001Invertibility of Toeplitz operators with polyanalytic symbols7938018569310.15352/aot.1812-1451ENAkaki TikaradzeUniversity of Toledo, USAJournal Article20181223For 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.http://www.aot-math.org/article_85693_62a43f8d788bd3e616b8b2a17c894450.pdf