Non-Hermitian Orthogonal Polynomials on a Trefoil

Non-Hermitian Orthogonal Polynomials on a Trefoil

We investigate asymptotic behavior of polynomials Q n ( z ) satisfying non-Hermitian orthogonality relations ∫ Δ s k Q n ( s ) ρ ( s ) d s = 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 includ...

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Veröffentlicht in:Constructive approximation 2024-04, Vol.59 (2), p.271-331
Hauptverfasser: Barhoumi, Ahmad B., Yattselev, Maxim L.
Format: Artikel
Sprache:eng
Schlagworte:
Analysis
Asymptotic properties
Mathematics
Mathematics and Statistics
Numerical Analysis
Orthogonality
Polynomials
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Zusammenfassung:We investigate asymptotic behavior of polynomials Q n ( z ) satisfying non-Hermitian orthogonality relations ∫ Δ s k Q n ( s ) ρ ( s ) d s = 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 .
ISSN:0176-4276
1432-0940
DOI:10.1007/s00365-023-09640-6