Eigenvalue problems for slice functions

Abstract

This paper addresses particular eigenvalue problems within the context of two quaternionic function theories. More precisely, we study two concrete classes of quaternionic eigenvalue problems, the first one for the slice derivative operator in the class of quaternionic slice-regular functions and the second one for the Cauchy-Riemann-Fueter operator in the class of axially monogenic functions. The two problems are related to each other by the four-dimensional Laplace operator and Fueter's Theorem. As an application of a particular case of second order eigenvalue problems, we obtain a representation of axially monogenic solutions for time-harmonic Helmholtz and stationary Klein-Gordon equations.

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• Slice regular functions on real alternative algebras
• Continuous slice functional calculus in quaternionic Hilbert spaces
• The algebra of slice functions
• On Appell Sets and the Fueter-Sce Mapping
• Slice regularity and harmonicity on Clifford algebras
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Cited by in corpus (2)

• Cauchy-Riemann operators and local slice analysis over real alternative algebras
• A local Cauchy integral formula for slice-regular functions