A Complete Orthogonal System of Spheroidal Monogenics

J. Morais2
Freiberg University of Mining and Technology,
Institute of Applied Analysis, Prueferstr. 9, 09596 Freiberg, Germany
Received 26 November, 2010; accepted in revised form 28 July, 2011
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 R3 . 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.


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