%0 Journal Article
%T Invertibility of Toeplitz operators with polyanalytic symbols
%J Advances in Operator Theory
%I Tusi Mathematical Research Group (TMRG)
%Z 2538-225X
%A Tikaradze, Akaki
%D 2019
%\ 10/01/2019
%V 4
%N 4
%P 793-801
%! Invertibility of Toeplitz operators with polyanalytic symbols
%K Toeplitz operator
%K the Bergman space
%K harmonic function
%R 10.15352/aot.1812-1451
%X 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.
%U http://www.aot-math.org/article_85693_62a43f8d788bd3e616b8b2a17c894450.pdf