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Keywords:
unit disk; polydisc; polynomial; Toeplitz operator; Bergman projection
unit disk; polydisc; polynomial; Toeplitz operator; Bergman projection
Summary:
Motivated by the relationship between the area of the image of the unit disk under a holomorphic mapping $h$ and that of $zh$, we study various $L^2$ norms for $T_{\varphi }(h)$, where $T_{\varphi }$ is the Toeplitz operator with symbol $\varphi $. In Theorem \ref {thm:Transitivity}, given polynomials $p$ and $q$ we find a symbol $\varphi $ such that $T_{\varphi }(p)=q$. We extend some of our results to the polydisc.
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