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On k-Hypermonogenic Functions and Their Mean Value Properties

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Original languageEnglish
Pages (from-to)311-325
Number of pages15
JournalComplex Analysis and Operator Theory
Issue number2
Early online date8 Mar 2015
Publication statusPublished - 2016
Publication typeA1 Journal article-refereed


We study a hyperbolic version of holomorphic functions to higher dimensions. In this frame work, a generalization of holomorphic functions are called (Formula presented.)-hypermonogenic functions. These functions are depending on several real variables and their values are in a Clifford algebra. They are defined in terms of hyperbolic Dirac operators. They are connected to harmonic functions with respect to the Riemannian metric (Formula presented.) in the same way as the usual harmonic function to holomorphic functions. We present the mean value property for (Formula presented.)-hypermonogenic functions and related results. Earlier the mean value properties has been proved for hypermonogenic functions. The key tools are the invariance properties of the hyperbolic metric.


  • Dirac operator, Hyperbolic metric, Hypermonogenic, Monogenic

Publication forum classification

Field of science, Statistics Finland