Non-Hermitian Orthogonal Polynomials on a Trefoil

Abstract

We investigate asymptotic behavior of polynomials $Q_n(z)$ satisfying non-Hermitian orthogonality relations $${\int }_{\Delta }{s}^k{Q}_n(s)\rho (s)ds=0,k\in \{0,\dots ,n-1\},$$ where $\Delta$ is a Chebotarëv (minimal capacity) contour connecting three non-collinear points and $\rho (s)$ is a Jacobi-type weight including a possible power-type singularity at the Chebotarëv center of $\Delta$.