A Complete Orthogonal System of Spheroidal Monogenics

Abstract

Abstract: During the past few years considerable attention has been given to the role played by monogenic functions in approximation theory. The main goal of the present paper is to construct a complete orthogonal system of monogenic polynomials as solutions of the Riesz system over prolate spheroids in R. This will be done in the spaces of square integrable functions over R. As a first step towards is that the orthogonality of the polynomials in question does not depend on the shape of the spheroids, but only on the location of the foci of the ellipse generating the spheroid. Some important properties of the system are briefly discussed.

Cite this paper

@inproceedings{Morais2012ACO, title={A Complete Orthogonal System of Spheroidal Monogenics}, author={J. Morais}, year={2012} }