On k-Hypermonogenic Functions and Their Mean Value Properties
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Details
| Original language | English |
|---|---|
| Pages (from-to) | 311-325 |
| Number of pages | 15 |
| Journal | Complex Analysis and Operator Theory |
| Volume | 10 |
| Issue number | 2 |
| Early online date | 8 Mar 2015 |
| DOIs | |
| Publication status | Published - 2016 |
| Publication type | A1 Journal article-refereed |
Abstract
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.
ASJC Scopus subject areas
Keywords
- Dirac operator, Hyperbolic metric, Hypermonogenic, Monogenic