# A 1-point poly-quadrature domain of order 1 not biholomorphic to a complete circular domain

A 1-point poly-quadrature domain of order 1 not biholomorphic to a complete circular domain It is known that if $$f: D_1 \rightarrow D_2$$ f : D 1 → D 2 is a polynomial biholomorphism with polynomial inverse and constant Jacobian then $$D_1$$ D 1 is a 1-point poly-quadrature domain (the Bergman span contains all holomorphic polynomials) of order 1 whenever $$D_2$$ D 2 is a complete circular domain. Bell conjectured that all 1-point poly-quadrature domains arise in this manner. In this note, we construct a 1-point poly-quadrature domain of order 1 that is not biholomorphic to any complete circular domain. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Analysis and Mathematical Physics Springer Journals

# A 1-point poly-quadrature domain of order 1 not biholomorphic to a complete circular domain

, Volume 9 (4) – Nov 2, 2018
4 pages

Publisher
Springer Journals
Subject
Mathematics; Analysis; Mathematical Methods in Physics
ISSN
1664-2368
eISSN
1664-235X
DOI
10.1007/s13324-018-0263-3
Publisher site
See Article on Publisher Site

### Abstract

It is known that if $$f: D_1 \rightarrow D_2$$ f : D 1 → D 2 is a polynomial biholomorphism with polynomial inverse and constant Jacobian then $$D_1$$ D 1 is a 1-point poly-quadrature domain (the Bergman span contains all holomorphic polynomials) of order 1 whenever $$D_2$$ D 2 is a complete circular domain. Bell conjectured that all 1-point poly-quadrature domains arise in this manner. In this note, we construct a 1-point poly-quadrature domain of order 1 that is not biholomorphic to any complete circular domain.

### Journal

Analysis and Mathematical PhysicsSpringer Journals

Published: Nov 2, 2018

### References

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