It is known that if \(f: D_1 \rightarrow D_2\) is a polynomial biholomorphism with polynomial inverse and constant Jacobian then \(D_1\) is a 1-point poly-quadrature domain (the Bergman span contains all holomorphic polynomials) of order 1 whenever \(D_2\) 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.

中文翻译：

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1阶1点多正交域，不是完整圆域的全同构

众所周知，如果\（f：D_1 \ rightarrow D_2 \）是具有多项式逆和常数Jacobian的多项式双全纯，则\（D_1 \）是一个1点多正交域（Bergman跨度包含所有全纯多项式）每当\（D_2 \）是一个完整的循环域时，顺序为1 。贝尔推测所有1点多正交域都以这种方式出现。在本说明中，我们构建了一个1点的1点多正交域，该域对任何完整的圆形域都不是全纯的。