7 citations · 13 across the 6 of their papers we have counts for
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Orthogonal polynomials on a class of planar algebraic curves
Marco Fasondini, Sheehan Olver, Yuan Xu
We construct bivariate orthogonal polynomials (OPs) on algebraic curves of the form in where and is a polynomial of arbitrary degree ,…
Sparse spectral methods for partial differential equations on spherical caps
Ben Snowball, Sheehan Olver
In recent years, sparse spectral methods for solving partial differential equations have been derived using hierarchies of classical orthogonal polynomials on intervals, disks, dis…
Orthogonal polynomials on planar cubic curves
Marco Fasondini, Sheehan Olver, Yuan Xu
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 define…
Sparse spectral and p-finite element methods for partial differential equations on disk slices and trapeziums
Ben Snowball, Sheehan Olver
Sparse spectral methods for solving partial differential equations have been derived in recent years using hierarchies of classical orthogonal polynomials on intervals, disks, and…
Orthogonal structure on a quadratic curve
Sheehan Olver, Yuan Xu
Orthogonal polynomials on quadratic curves in the plane are studied. These include orthogonal polynomials on ellipses, parabolas, hyperbolas, and two lines. For an integral with re…