Contragenic Functions on Spheroidal Domains
R. Garc\'ia Ancona, J. Morais, R. Michael Porter
TL;DR
This paper develops polynomial bases for harmonic functions on spheroidal domains that are orthogonal to monogenic and antimonogenic functions, advancing mathematical tools for spheroidal harmonic analysis.
Contribution
It introduces new polynomial bases for harmonic functions on spheroids that are orthogonal to monogenic and antimonogenic functions, filling a gap in spheroidal harmonic analysis.
Findings
Constructed orthogonal polynomial bases for spheroidal harmonic functions.
Extended harmonic analysis tools to prolate and oblate spheroids.
Provided mathematical framework for spheroidal harmonic function spaces.
Abstract
We construct bases of polynomials for the spaces of square-integrable harmonic functions which are orthogonal to the monogenic and antimonogenic -valued functions defined in a prolate or oblate spheroid.
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