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Comments on an Orthogonal Family of Monogenic Functions on Spheroidal Domains

  • Joaõ MoraisEmail author
Chapter
Part of the Trends in Mathematics book series (TM)

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.

Keywords

Quaternionic analysis Spherical harmonics Spheroidal harmonics Monogenic functions 

Mathematics Subject Classification (2010)

Primary 30G35 Secondary 30C65 

Notes

Acknowledgement

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

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of MathematicsITAMMexico CityMexico

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