A plane domain is a log-weighted quadrature domain if and only if, when simply connected, the outer factor of its Riemann map is the exponential of a rational function.
On the Faber Transform and Efficient Numerical Rational Approximation
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Analysis of Log-Weighted Quadrature Domains
A plane domain is a log-weighted quadrature domain if and only if, when simply connected, the outer factor of its Riemann map is the exponential of a rational function.