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A. Legg (2018)
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(2017)
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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.
Analysis and Mathematical Physics – Springer Journals
Published: Nov 2, 2018
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