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Recent Progress on Spheroidal Monogenic Functions

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Current Trends in Analysis and Its Applications

Part of the book series: Trends in Mathematics ((RESPERSP))

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Abstract

Monogenic function theories are considered as generalizations of the holomorphic function theory in the complex plane to higher dimensions and are refinements of the harmonic analysis based on the Laplace operator’s factorizations. The construction of spherical monogenic functions has been studied for decades with different methods. Recently, orthogonal monogenic bases are developed for spheroidal reference domains, first by J. Morais and later by others. This survey will go through the construction of spheroidal monogenic functions and discuss up-to-date results.

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Acknowledgements

The author acknowledges the financial support of MOET-Vietnam & DAAD and Prof. K. Gürlebeck and Dr. J. Morais for the valuable discussions.

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Authors and Affiliations

  1. Inst. f. Math. u. Phys., Coudraystr. 13B, 99423, Weimar, Germany

    Hung Manh Nguyen

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  1. Hung Manh Nguyen
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Correspondence to Hung Manh Nguyen .

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Editors and Affiliations

  1. Dept. of Computer Sc. & Comp. Methods, Pedagogical University, Kraków, Poland

    Vladimir V. Mityushev

  2. Imperial College London, London, United Kingdom

    Michael V. Ruzhansky

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Nguyen, H.M. (2015). Recent Progress on Spheroidal Monogenic Functions. In: Mityushev, V., Ruzhansky, M. (eds) Current Trends in Analysis and Its Applications. Trends in Mathematics(). Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-12577-0_54

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