Fundamental solution of k-hyperbolic harmonic functions in odd spaces
Research output: Contribution to journal › Article › Scientific › peer-review
|Journal||Journal of Physics: Conference Series|
|Publication status||Published - 13 Apr 2015|
|Publication type||A1 Journal article-refereed|
We study k-hyperbolic harmonic functions in the upper half space . The operator is the Laplace-Beltrami operator with respect to the Riemannian metric . In case k = n - 1 the Riemannian metric is the hyperbolic distance of Poincare upper half space. The proposed functions are connected to the axially symmetric potentials studied notably by Weinstein, Huber and Leutwiler. We present the fundamental solution in case n is even using the hyperbolic metric. The main tool is the transformation of k-hyperbolic harmonic functions to eigenfunctions of the hyperbolic Laplace operator.