Function Theory for Laplace and Dirac-Hodge Operators in Hyperbolic SPace
Abstract
We develop basic properties of solutions to the Dirac-Hodge and Laplace equations in upper half space endowed with the hyperbolic metric. Solutions to the Dirac-Hodge equation are called hypermonogenic functions while solutions to this version of Laplace's equation are called hyperbolic harmonic functions. We introduce a Borel-Pompeiu formula and a Green's formula for hyperbolic harmonic functions. Using a Cauchy Integral formula we are able to introduce Hardy spaces of solutions to the Dirac-Hodge equation. We also provide new arguments describing the conformal covariance of hypermonogenic functions and invariance of hyperbolic harmonic functions. We introduce intertwining operators for the Dirac-Hodge operator and hyperbolic Laplacian.
Cite
@article{arxiv.math/0407192,
title = {Function Theory for Laplace and Dirac-Hodge Operators in Hyperbolic SPace},
author = {Yuying Qiao and Swanhild Bernstein and Sirkka-Liisa Eriksson and John Ryan},
journal= {arXiv preprint arXiv:math/0407192},
year = {2016}
}
Comments
23 pages