Quadrature domains in \mathbb Cⁿ

2014/06/13 by Pranav Haridas, Haridas, Pranav, Kaushal Verma +1
Mathematics · #Algebraic and Geometric Analysis #Analytic Number Theory Research #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1406.3449

openalex publication_date 2014/06/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove two density theorems for quadrature domains in ℂⁿ, n ≥ 2. It is shown that quadrature domains are dense in the class of all product domains of the form D × Ω, where D ⊂ ℂ^n-1 is a smoothly bounded domain satisfying Bell's Condition R and Ω⊂ ℂ is a smoothly bounded domain and also in the class of all smoothly bounded complete Hartogs domains in ℂ².

Citations

• Domains on which analytic functions satisfy quadrature identities

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