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 L 2 norms for T ϕ ( h ), where T ϕ is the Toeplitz operator with symbol ϕ . In Theorem 2.1, given polynomials p and q we find a symbol ϕ such that T ϕ ( p ) =...

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Bibliographic Details
Published in:Czechoslovak mathematical journal 2024, Vol.74 (3), p.817-838
Main Authors: Çelik, Mehmet, Duane-Tessier, Luke, Rodriguez, Ashley Marcial, Rodriguez, Daniel, Shaw, Aden
Format: Article
Language:English
Subjects:
Analysis
Convex and Discrete Geometry
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Operators (mathematics)
Ordinary Differential Equations
Polynomials
Online Access:Get full text
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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 ϕ ( h ), where T ϕ is the Toeplitz operator with symbol ϕ . In Theorem 2.1, given polynomials p and q we find a symbol ϕ such that T ϕ ( p ) = q . We extend some of our results to the polydisc.
ISSN:0011-4642
1572-9141
DOI:10.21136/CMJ.2024.0023-24