Mehmet Çelik, Luke Duane-Tessier, Ashley Marcial Rodriguez, Daniel Rodriguez, Aden Shaw
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Area differences under analytic maps and operators
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 L2 norms for Tϕ(h), where Tϕ is the Toeplitz operator with symbol ϕ. In Theorem 2.1, given polynomials p and q we find a symbol ϕ such that Tϕ(p) = q. We extend some of our results to the polydisc.
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