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Orthogonal polynomials in and on a quadratic surface of revolution


Authors: Sheehan Olver and Yuan Xu
Journal: Math. Comp. 89 (2020), 2847-2865
MSC (2010): Primary 42C05, 42C10, 65D15, 65D32
DOI: https://doi.org/10.1090/mcom/3544
Published electronically: June 5, 2020
MathSciNet review: 4136549
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Abstract | References | Similar Articles | Additional Information

Abstract: We present explicit constructions of orthogonal polynomials inside quadratic bodies of revolution, including cones, hyperboloids, and paraboloids. We also construct orthogonal polynomials on the surface of quadratic surfaces of revolution, generalizing spherical harmonics to the surface of a cone, hyperboloid, and paraboloid. We use this construction to develop cubature and fast approximation methods.


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References
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Additional Information

Sheehan Olver
Affiliation: Department of Mathematics, Imperial College, London, United Kingdom
MR Author ID: 783322
ORCID: 0000-0001-6920-0826
Email: s.olver@imperial.ac.uk

Yuan Xu
Affiliation: Department of Mathematics, University of Oregon, Eugene, Oregon 97403-1222.
MR Author ID: 227532
Email: yuan@uoregon.edu

Keywords: Orthogonal polynomials, quadratic surface of revolution, cubature rule, approximation method
Received by editor(s): June 25, 2019
Received by editor(s) in revised form: February 4, 2020
Published electronically: June 5, 2020
Additional Notes: The first author was supported by the Leverhulme Trust Research Project Grant RPG-2019-144 “Constructive approximation theory on and inside algebraic curves and surfaces”.
This work was supported by EPSRC grant no EP/K032208/1.
Article copyright: © Copyright 2020 American Mathematical Society