Geodesic
Potential theory of one-dimensional geometric stable processes
Tomasz Grzywny 1   ; Michał Ryznar 1
1 Institute of Mathematics and Computer Sciences Wrocław University of Technology Wybrzeże Wyspiańskiego 27 50-370 Wrocław, Poland
Colloquium Mathematicum, Tome 129 (2012) no. 1, pp. 7-40 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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The purpose of this paper is to find optimal estimates for the Green function and the Poisson kernel for a half-line and intervals of the geometric stable process with parameter $\alpha\in(0,2]$. This process has an infinitesimal generator of the form $-\log(1+(-{\mit\Delta})^{\alpha/2})$. As an application we prove the global scale invariant Harnack inequality as well as the boundary Harnack principle.
DOI : 10.4064/cm129-1-2
Keywords: purpose paper optimal estimates green function poisson kernel half line intervals geometric stable process parameter alpha process has infinitesimal generator form log mit delta alpha application prove global scale invariant harnack inequality boundary harnack principle

Tomasz Grzywny  1   ; Michał Ryznar  1

1 Institute of Mathematics and Computer Sciences Wrocław University of Technology Wybrzeże Wyspiańskiego 27 50-370 Wrocław, Poland 
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Tomasz Grzywny; Michał Ryznar. Potential theory of one-dimensional geometric stable processes. Colloquium Mathematicum, Tome 129 (2012) no. 1, pp. 7-40. doi: 10.4064/cm129-1-2

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