Non-Hermitian Orthogonal Polynomials on a Trefoil
We investigate asymptotic behavior of polynomials $ Q_n(z) $ satisfying non-Hermitian orthogonality relations $$ \int_Δs^kQ_n(s)ρ(s)ds =0, \quad k\in\{0,\ldots,n-1\}, $$ where $ Δ$ is a Chebotarëv (minimal capacity) contour connecting three non-collinear points and $ ρ(s) $ is a Jacobi-type weight including a possible power-type singularity at the Chebotarëv center of $ Δ$.
math.CA↗