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.

Eigenvalue problems for slice functions / Krausshar, ROLF SÖREN; Perotti, Alessandro. - In: ANNALI DI MATEMATICA PURA ED APPLICATA. - ISSN 1618-1891. - 2022:(2022), pp. [1-30]. [10.1007/s10231-022-01208-8]

Eigenvalue problems for slice functions

PEROTTI, ALESSANDRO
2022

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.
Krausshar, ROLF SÖREN; Perotti, Alessandro
Eigenvalue problems for slice functions / Krausshar, ROLF SÖREN; Perotti, Alessandro. - In: ANNALI DI MATEMATICA PURA ED APPLICATA. - ISSN 1618-1891. - 2022:(2022), pp. [1-30]. [10.1007/s10231-022-01208-8]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/299905
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