A 1-point Quadrature domain of order 1 not biholomorphic to a balanced domain

2018/07/23 by Pranav Haridas, Haridas, Pranav, Jaikrishnan Janardhanan +1
Mathematics · #32A07 #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.1807.08689

openalex publication_date 2018/07/23 · openalex created_date 2019/02/21 · openalex updated_date 2026/07/28

Abstract

It is known that if f: D₁ → D₂ is a polynomial biholomorphism with polynomial inverse and constant Jacobian then D₁ is a 1-point Quadrature domain (the Bergman span contains all holomorphic polynomials) of order 1 whenever D₂ is a balanced domain. Bell conjectured that all 1-point Quadrature domains arise in this manner. In this note, we construct a 1-point Quadrature domain of order 1 that is not biholomorphic to any balanced domain.

Citations

• Domains on which analytic functions satisfy quadrature identities

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