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Intrinsic ultracontractivity for symmetric stable processes

Tadeusz Kulczycki
- 01 Jan 1998 - 
- Vol. 46, Iss: 3, pp 325-334
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This article is published in Bulletin of The Polish Academy of Sciences Mathematics.The article was published on 1998-01-01 and is currently open access. It has received 85 citations till now.

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Heat kernel estimates for the Dirichlet fractional Laplacian

Zhen-Qing Chen, +2 more
- 15 Aug 2010 - 
TL;DR: In this article, the Dirichlet heat kernel of a non-local operator on open sets has been studied and sharp two-sided estimates for the heat kernel have been obtained for C 1.1 open sets.
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Estimates of Green Function for Relativistic α-Stable Process

MichaŁ Ryznar
- 01 Aug 2002 - 
TL;DR: In this paper, the authors derived sharp estimates for the Green function of the relativistic α-stable process on CSpaceEngineers1,1 domains using these estimates they provided lower and upper bounds for the Poisson kernel.
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Two-sided eigenvalue estimates for subordinate processes in domains

Zhen-Qing Chen, +1 more
- 01 Sep 2005 - 
TL;DR: In this paper, it was shown that if the eigenvalues of the generators of the subprocess of a process X killed upon leaving D and of the process X D respectively are the same as those of the generator of X and of X D, then the processes X := {XSt,t 0} and (X D ) := [X Dt,t0], respectively, are called the subordinate processes X and X D, respectively.
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Eigenvalues of the fractional Laplace operator in the interval

Mateusz Kwaśnicki, +1 more
- 01 Mar 2012 - 
TL;DR: In this article, a two-term Weyl-type asymptotic law for the eigenvalues of the one-dimensional fractional Laplace operator ( − Δ ) α / 2 ( α ∈ ( 0, 2 ) ) in the interval ( − 1, 1 ) is given: the n -th eigenvalue is equal to ( n π / 2 − ( 2 − α ) π/ 8 ) α + O ( 1 / n ).
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Heat kernel estimates for the fractional Laplacian with Dirichlet conditions

Krzysztof Bogdan, +2 more
- 01 Sep 2010 - 
TL;DR: In this paper, the authors give sharp estimates for the heat kernel of the fractional Laplacian with Dirichlet condition for a general class of domains including Lipschitz domains.