Bessel Potentials, Hitting Distributions and Green Functions
| dc.creator | Byczkowski, T. | |
| dc.creator | Ryznar, M. | |
| dc.creator | Malecki, J. | |
| dc.date | 2006-12-07 | |
| dc.date.accessioned | 2026-07-07T07:34:43Z | |
| dc.date.available | 2026-07-07T07:34:43Z | |
| dc.description | The purpose of this paper is to find explicit formulas for basic objects pertaining the local potential theory of the operator $(I-Δ)^{α/2}$, $0<α<2$. The potential theory of this operator is based on Bessel potentials $J_α=(I-Δ)^{-α/2}$. We compute the {\it harmonic measure} of the half-space and write a concise form of the corresponding {\it Green function} for the operator $(I-Δ)^{α/2}$. To achieve this we analyze the so-called {\it relativistic $α$-stable process} on $\R^d$ space, killed when exiting the half-space. In terms of this process we are dealing here with the 1-{\it potential theory} or, equivalently, potential theory of Schr{ö}dinger operator based on the generator of the process with Kato's potential $q=-1$. | |
| dc.identifier | https://arxiv.org/abs/math/0612176 | |
| dc.identifier | http://arxiv.org/abs/math/0612176 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/119864 | |
| dc.subject | Probability | |
| dc.subject | 60J65 | |
| dc.title | Bessel Potentials, Hitting Distributions and Green Functions | |
| dc.type | text |