Three-term recurrence relation for polynomials orthogonal with respect to harmonic measure (Q2754794)

Let \(G\subset \mathbb C\) be a bounded, simply connected domain, and let \(\{P_n\}\) be a system of polynomials orthonormal in the Hardy space \(H^2(G)\). It is shown that \(\{P_n\}\) satisfies a three-term relation (similar to the classical relation for orthogonal polynomials on an interval) if and only if \(\partial G\) is an ellipse. For this case a version of the Christoffel-Darboux identity is established.