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Comments on an Orthogonal Family of Monogenic Functions on Spheroidal Domains

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Topics in Clifford Analysis

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Abstract

The problem of building an orthogonal basis for the space of square-integrable harmonic functions defined in a spheroidal (either oblate or prolate) domain leads to special functions, which provide an elegant analysis of a variety of physical problems. Many generalizations of these ideas in the context of Quaternionic Analysis possess a similar elegant mathematical structure. A brief descriptive review is given of these developments.

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Acknowledgement

The author’s work is supported by the Asociación Mexicana de Cultura, A. C.

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  1. Department of Mathematics, ITAM, Mexico City, Mexico

    Joaõ Morais

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  1. Joaõ Morais
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Correspondence to Joaõ Morais .

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  1. Institut für Angewandte Analysis, TU Bergakademie Freiberg, Freiberg, Germany

    Swanhild Bernstein

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Morais, J. (2019). Comments on an Orthogonal Family of Monogenic Functions on Spheroidal Domains. In: Bernstein, S. (eds) Topics in Clifford Analysis. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-23854-4_12

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