# Quadrature Domains in $${{\mathbb C}}^n$$ C n

Quadrature Domains in $${{\mathbb C}}^n$$ C n We prove two density theorems for quadrature domains in $$\mathbb {C}^n$$ C n , $$n \ge 2$$ n ≥ 2 . It is shown that quadrature domains are dense in the class of all product domains of the form $$D \times \Omega$$ D × Ω , where $$D \subset \mathbb {C}^{n-1}$$ D ⊂ C n - 1 is a smoothly bounded domain satisfying Bell’s Condition R and $$\Omega \subset \mathbb {C}$$ Ω ⊂ C is a smoothly bounded domain and also in the class of all smoothly bounded complete Hartogs domains in $$\mathbb {C}^2$$ C 2 . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Methods and Function Theory Springer Journals

# Quadrature Domains in $${{\mathbb C}}^n$$ C n

, Volume 15 (1) – Sep 20, 2014
17 pages

Publisher
Springer Journals
Subject
Mathematics; Analysis; Computational Mathematics and Numerical Analysis; Functions of a Complex Variable
ISSN
1617-9447
eISSN
2195-3724
DOI
10.1007/s40315-014-0090-y
Publisher site
See Article on Publisher Site

### Abstract

We prove two density theorems for quadrature domains in $$\mathbb {C}^n$$ C n , $$n \ge 2$$ n ≥ 2 . It is shown that quadrature domains are dense in the class of all product domains of the form $$D \times \Omega$$ D × Ω , where $$D \subset \mathbb {C}^{n-1}$$ D ⊂ C n - 1 is a smoothly bounded domain satisfying Bell’s Condition R and $$\Omega \subset \mathbb {C}$$ Ω ⊂ C is a smoothly bounded domain and also in the class of all smoothly bounded complete Hartogs domains in $$\mathbb {C}^2$$ C 2 .

### Journal

Computational Methods and Function TheorySpringer Journals

Published: Sep 20, 2014

### References

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