Non-Hermitian Orthogonal Polynomials on a Trefoil

2023/03/29 by Ahmad Barhoumi, Barhoumi, Ahmad B., Maxim L. Yattselev +1 · 1 citation
Chemistry · Physics and Astronomy · #41A20 #41A21 #42C05 #Classical Analysis and ODEs (math.CA) #Crystal structures of chemical compounds #Crystallography and molecular interactions #FOS: Mathematics #Quantum Mechanics and Non-Hermitian Physics

paper · pdf · doi:10.48550/arxiv.2303.17037

openalex publication_date 2023/03/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate asymptotic behavior of polynomials Q_n(z) satisfying non-Hermitian orthogonality relations ∫_Δs^kQ_n(s)ρ(s)ds =0, k∈\0,…,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.

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