Abstract
We give sufficient conditions for nonlocal perturbations of integral kernels to be locally in time comparable with the original kernel.
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References
Bogdan, K., Byczkowski, T., Kulczycki, T., Ryznar, M., Song, R., and Vondraček, Z. Potential analysis of stable processes and its extensions, vol. 1980 of Lecture Notes in Mathematics. Springer-Verlag, Berlin, 2009. Edited by Piotr Graczyk and Andrzej Stos.
Bogdan, K., Hansen, W., and Jakubowski, T. Time-dependent Schrödinger perturbations of transition densities. Studia Math. 189, 3 (2008), 235–254.
Bogdan, K., Hansen, W., and Jakubowski, T. Localization and Schrödinger Perturbations of Kernels. Potential Anal. 39, 1 (2013), 13–28.
Bogdan, K., and Jakubowski, T. Estimates of the Green function for the fractional Laplacian perturbed by gradient. Potential Analysis 36 (2012), 455–481.
Bogdan, K., and Jakubowski, T. Estimates of the Green function for the fractional Laplacian perturbed by gradient. Potential Anal. 36, 3 (2012), 455–481.
Bogdan, K., Jakubowski, T., and Sydor, S. Estimates of perturbation series for kernels. J. Evol. Equ. 12, 4 (2012), 973–984.
Chen, Z.-Q., Kim, P., and Song, R. Stability of Dirichlet heat kernel estimates for non-local operators under Feynman-Kac perturbation. ArXiv e-prints (Dec. 2011).
Chen, Z.-Q., and Kumagai, T. Heat kernel estimates for stable-like processes on d-sets. Stochastic Process. Appl. 108, 1 (2003), 27–62.
Chen, Z.-Q., and Wang, J.-M. Perturbation by non-local operators. ArXiv e-prints (Dec. 2013).
Dellacherie, C., and Meyer, P.-A. Probabilities and potential. C, vol. 151 of North-Holland Mathematics Studies. North-Holland Publishing Co., Amsterdam, 1988. Potential theory for discrete and continuous semigroups, Translated from the French by J. Norris.
Grzywny, T., and Ryznar, M. Estimates of Green functions for some perturbations of fractional Laplacian. Illinois J. Math. 51, 4 (2007), 1409–1438.
Kaleta, K., and Sztonyk, P. Upper estimates of transition densities for stable-dominated semigroups. ArXiv e-prints (Sept. 2012).
Kim, P., and Lee, Y.-R. Generalized 3G theorem and application to relativistic stable process on non-smooth open sets. J. Funct. Anal. 246, 1 (2007), 113–143.
Knopova, V., and Kulik, A. Parametrix construction for certain Lévy-type processes and applications. ArXiv e-prints (July 2013).
Sato, K.-I. Lévy processes and infinitely divisible distributions, vol. 68 of Cambridge Studies in Advanced Mathematics. Cambridge University Press, Cambridge, 1999. Translated from the 1990 Japanese original, Revised by the author.
Sztonyk, P. Transition density estimates for jump Lévy processes. Stochastic Process. Appl. 121, 6 (2011), 1245–1265.
Zhang, X. Heat kernels and analyticity of non-symmetric Lévy diffusion semigroups. ArXiv e-prints (June 2013).
Acknowledgments
We thank Tomasz Jakubowski for discussions and suggestions. The research was partially supported by grant MNiSW N N201 397137 and NCN 2012/07/N/ST1/03285.
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Bogdan, K., Sydor, S. (2015). On Nonlocal Perturbations of Integral Kernels. In: Banasiak, J., Bobrowski, A., Lachowicz, M. (eds) Semigroups of Operators -Theory and Applications. Springer Proceedings in Mathematics & Statistics, vol 113. Springer, Cham. https://doi.org/10.1007/978-3-319-12145-1_2
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DOI: https://doi.org/10.1007/978-3-319-12145-1_2
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