Mapping Properties of Quadrature Domains in Several Complex Variables
Alan R. Legg
TL;DR
This paper explores the properties of quadrature domains in multiple complex variables using the Bergman kernel, extending known planar results to higher dimensions.
Contribution
It generalizes biholomorphic mapping properties of quadrature domains from one complex variable to several complex variables.
Findings
Bergman kernel used to analyze quadrature domains in multiple variables
Extension of planar biholomorphic mapping properties to higher dimensions
Advances understanding of the structure of quadrature domains in several complex variables
Abstract
We make use of the Bergman kernel function to study quadrature domains for square-integrable holomorphic functions of several variables. Emphasis is given to generalizing biholomorphic mapping properties of planar quadrature domains to the several-dimensional setting.
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Taxonomy
TopicsHolomorphic and Operator Theory · Algebraic and Geometric Analysis · Meromorphic and Entire Functions