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Potential theory of one-dimensional geometric stable processes

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Grzywny T., Ryznar M.
Colloquium Mathematicum
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2012
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tom 129
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nr 1
7-40
EN
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 α ∈ (0,2]. This process has an infinitesimal generator of the form $-log(1+(-Δ)^{α/2})$. As an application we prove the global scale invariant Harnack inequality as well as the boundary Harnack principle.
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Applied Mathematics on joint Meeting of UMI-SIMAI-PTM, September 17-20, 2018

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Grzywny T., Bogdan K.
Mathematica Applicanda
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2018
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tom 46
|
nr 2
EN
The 2018 Forum of Mathematician was organized with cooperation of Italian Mathematical Union (Union e Matematica Italiana) and the Italian Society of Industrial and Applied Mathematics (Società Italiana di Matematica Applicata e Industriale). The meeting aims at continuation of the tradition of bilateral meetings held in the last years by the Polish Mathematical Society together with other national societies. This forum does not exclude the participation of mathematicians from other countries. The Forum in Wroclaw also hosted a large group of participants from outside Poland and Italy. The meeting was hosted by the Faculty Mathematics and Computer Science of the University of Wrocław and the Faculty of of Pure and Applied Mathematics of Wrocław University of Science and Technology. It was the fourth bilateral symposium of PTM after the Second World War (cf. Duda(2018)): AMS-PTM Joint Meeting (Warsaw) in 2007, IMU-PTM Joint meeting (Łódź) in 2011 and DMV-PTM Joint Metting (Poznań) in 2014.
3
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Heat kernel of fractional Laplacian in cones

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Bogdan K., Grzywny T.
Colloquium Mathematicum
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2010
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tom 118
|
nr 2
365-377
EN
We give sharp estimates for the transition density of the isotropic stable Lévy process killed when leaving a right circular cone.
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