Bessel potentials, hitting distributions and Green functions
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- by T. Byczkowski, J. Małecki and M. Ryznar PDF
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Abstract:
The purpose of the paper is to find explicit formulas for basic objects pertaining to the potential theory of the operator $(I-\Delta )^{\alpha /2}$, which is based on Bessel potentials $J_{\alpha }=(I-\Delta )^{-\alpha /2}$, $0<\alpha <2$. We compute the harmonic measure of the half-space and obtain a concise form for the corresponding Green function of the operator $(I-\Delta )^{\alpha /2}$. As an application we provide sharp estimates for the Green function of the half-space for the relativistic process.References
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Additional Information
- T. Byczkowski
- Affiliation: Institute of Mathematics and Computer Sciences, Wrocław University of Technology, ul. Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland
- Email: tomasz.byczkowski@pwr.wroc.pl
- J. Małecki
- Affiliation: Institute of Mathematics and Computer Sciences, Wrocław University of Technology, ul. Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland
- ORCID: 0000-0003-2250-5010
- Email: jacek.malecki@pwr.wroc.pl
- M. Ryznar
- Affiliation: Institute of Mathematics and Computer Sciences, Wrocław University of Technology, ul. Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland
- Email: michal.ryznar@pwr.wroc.pl
- Received by editor(s): February 6, 2007
- Received by editor(s) in revised form: October 5, 2007
- Published electronically: April 10, 2009
- Additional Notes: This research was supported by DBN Grant 1P03A 020 28 and the second author was additionally supported by DBN Grant N N201 4100 33
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 361 (2009), 4871-4900
- MSC (2000): Primary 60J65; Secondary 60J60
- DOI: https://doi.org/10.1090/S0002-9947-09-04657-1
- MathSciNet review: 2506430