General Integral Formulas for k-hyper-mono-genic Functions
Research output: Contribution to journal › Article › Scientific › peer-review
Details
| Original language | English |
|---|---|
| Pages (from-to) | 99-110 |
| Number of pages | 12 |
| Journal | Advances in Applied Clifford Algebras |
| Volume | 27 |
| Issue number | 1 |
| Early online date | 22 Dec 2015 |
| DOIs | |
| Publication status | Published - 2017 |
| Publication type | A1 Journal article-refereed |
Abstract
We are studying a function theory of k-hypermonogenic functions connected to k-hyperbolic harmonic functions that are harmonic with respect to the hyperbolic Riemannian metric k2=xn2k1-n(dx02+⋯+dxn2)in the upper half space R+n+1={(x0,…,xn)|xi∈R,xn>0}. The function theory based on this metric is important, since in case k= n- 1 , the metric is the hyperbolic metric of the Poincaré upper half space and Leutwiler noticed that the power function xm(m∈N0), calculated using Clifford algebras, is a conjugate gradient of a hyperbolic harmonic function. We find a fundamental k-hyperbolic harmonic function. Using this function we are able to find kernels and integral formulas for k-hypermonogenic functions. Earlier these results have been verified for hypermonogenic functions (k= n- 1) and for k-hyperbolic harmonic functions in odd dimensional spaces.