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arXiv · 2303.17037

Non-Hermitian Orthogonal Polynomials on a Trefoil

Ahmad B. Barhoumi·Maxim L. Yattselev
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Abstract

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

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Ahmad B. Barhoumi, Maxim L. Yattselev. 2023-03-29. Non-Hermitian Orthogonal Polynomials on a Trefoil. https://arxiv.org/abs/2303.17037

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