Orthogonal polynomials on planar cubic curves

2020/11/21 by Marco Fasondini, Sheehan Olver, Fasondini, Marco +3 · 2 citations
Mathematics · Physics and Astronomy · #33C50 #35C10 #42C05 #42C10 #Classical Analysis and ODEs (math.CA) #Electromagnetic Scattering and Analysis #FOS: Mathematics #Mathematical functions and polynomials #Numerical Analysis (math.NA) #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.2011.10884

openalex publication_date 2020/11/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Orthogonal polynomials in two variables on cubic curves are considered, including the case of elliptic curves. For an integral with respect to an appropriate weight function defined on a cubic curve, an explicit basis of orthogonal polynomials is constructed in terms of two families of orthogonal polynomials in one variable. We show that these orthogonal polynomials can be used to approximate functions with cubic and square root singularities, and demonstrate their usage for solving differential equations with singular solutions.

Citations

• A Fast and Well-Conditioned Spectral Method

Cited by

• Elliptic orthogonal polynomials and OPRL
• Recurrence relations and the Christoffel-Darboux formula for elliptic orthogonal polynomials

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