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Fueter Mapping Theorem in Hypercomplex Analysis

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Operator Theory

Abstract

Fueter’s Theorem offers a method that conveys certain holomorphic functions in one complex variable to quaternionic regular (monogenic) functions. Ever since the theorem was proved in 1935, it underwent several main generalizations. Those are not only based on its own interest, but also motivated by applications found in other areas of mathematics, such as functional calculus of operators. This article serves as a survey on Fueter’s Theorem, its generalizations and applications.

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Acknowledgements

The author wishes to sincerely thank I. Sabadini, F. Colombo, and D. Peña Peña for helpful information and remarks on the subject which greatly contribute to the writing out of this essay.

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Authors and Affiliations

  1. Faculty of Science and Technology, University of Macau, Av. Padre Tomás Pereira, Taipa, Macau, China

    Tao Qian

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  1. Tao Qian
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Correspondence to Tao Qian .

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Editors and Affiliations

  1. Ben-Gurion University of the Negev, Department of Mathematics, Beer-Sheva, Israel

    Daniel Alpay

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Qian, T. (2014). Fueter Mapping Theorem in Hypercomplex Analysis. In: Alpay, D. (eds) Operator Theory. Springer, Basel. https://doi.org/10.1007/978-3-0348-0692-3_28-1

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  • DOI: https://doi.org/10.1007/978-3-0348-0692-3_28-1

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  • Online ISBN: 978-3-0348-0692-3

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