Area differences under analytic maps and operators

Mehmet Çelik; Luke Duane-Tessier; Ashley Marcial Rodriguez; Daniel Rodriguez; Aden Shaw

Czechoslovak Mathematical Journal (2024)

  • Volume: 74, Issue: 3, page 817-838
  • ISSN: 0011-4642

Abstract

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Motivated by the relationship between the area of the image of the unit disk under a holomorphic mapping h and that of z h , we study various L 2 norms for T ϕ ( h ) , where T ϕ is the Toeplitz operator with symbol ϕ . In Theorem , 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.

How to cite

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Çelik, Mehmet, et al. "Area differences under analytic maps and operators." Czechoslovak Mathematical Journal 74.3 (2024): 817-838. <http://eudml.org/doc/299309>.

@article{Çelik2024,
abstract = {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 , 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.},
author = {Çelik, Mehmet, Duane-Tessier, Luke, Marcial Rodriguez, Ashley, Rodriguez, Daniel, Shaw, Aden},
journal = {Czechoslovak Mathematical Journal},
keywords = {unit disk; polydisc; polynomial; Toeplitz operator; Bergman projection},
language = {eng},
number = {3},
pages = {817-838},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Area differences under analytic maps and operators},
url = {http://eudml.org/doc/299309},
volume = {74},
year = {2024},
}

TY - JOUR
AU - Çelik, Mehmet
AU - Duane-Tessier, Luke
AU - Marcial Rodriguez, Ashley
AU - Rodriguez, Daniel
AU - Shaw, Aden
TI - Area differences under analytic maps and operators
JO - Czechoslovak Mathematical Journal
PY - 2024
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 74
IS - 3
SP - 817
EP - 838
AB - 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 , 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.
LA - eng
KW - unit disk; polydisc; polynomial; Toeplitz operator; Bergman projection
UR - http://eudml.org/doc/299309
ER -

References

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