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Minimal thinness with respect to symmetric Lévy processes


Authors: Panki Kim, Renming Song and Zoran Vondraček
Journal: Trans. Amer. Math. Soc. 368 (2016), 8785-8822
MSC (2010): Primary 60J50, 31C40; Secondary 31C35, 60J45, 60J75
DOI: https://doi.org/10.1090/tran/6613
Published electronically: February 12, 2016
MathSciNet review: 3551589
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Abstract: Minimal thinness is a notion that describes the smallness of a set at a boundary point. In this paper, we provide tests for minimal thinness at finite and infinite minimal Martin boundary points for a large class of purely discontinuous symmetric Lévy processes.


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Additional Information

Panki Kim
Affiliation: Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University, Building 27, 1 Gwanak-ro, Gwanak-gu, Seoul 151-747, Republic of Korea
Email: pkim@snu.ac.kr

Renming Song
Affiliation: Department of Mathematics, University of Illinois, Urbana, Illinois 61801
Email: rsong@math.uiuc.edu

Zoran Vondraček
Affiliation: Department of Mathematics, University of Zagreb, Zagreb, Croatia
Email: vondra@math.hr

DOI: https://doi.org/10.1090/tran/6613
Keywords: Minimal thinness, symmetric L\'evy process, unimodal L\'evy process, boundary Harnack principle, Green function, Martin kernel, quasi-additivity, Wiener-type criterion
Received by editor(s): May 1, 2014
Received by editor(s) in revised form: October 5, 2014, November 1, 2014, and November 17, 2014
Published electronically: February 12, 2016
Additional Notes: The work of Panki Kim was supported by the National Research Foundation of Korea (NRF) grant funded by the Korean government (MEST) (NRF-2013R1A2A2A01004822)
The research of Renming Song was supported in part by a grant from the Simons Foundation (208236)
The research of Zoran Vondraček was supported in part by the Croatian Science Foundation under the project 3526
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