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Fueter Mapping Theorem in Hypercomplex Analysis

In: Operator Theory

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  • Tao Qian

    (University of Macau, Faculty of Science and Technology)

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.

Suggested Citation

  • Tao Qian, 2015. "Fueter Mapping Theorem in Hypercomplex Analysis," Springer Books, in: Daniel Alpay (ed.), Operator Theory, edition 127, chapter 52, pages 1491-1507, Springer.
    • Handle: RePEc:spr:sprchp:978-3-0348-0667-1_28
    DOI: 10.1007/978-3-0348-0667-1_28
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