Trace estimates for stable processes

Probability Theory and Related Fields

Volumn 142, Issue 3-4, 2008, Pages 313-338

  Bañuelos, Rodrigo ^a   Kulczycki, Tadeusz ^b  

^a PURDUE UNIVERSITY   (United States)

^b WROCLAW UNIVERSITY OF TECHNOLOGY   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 49749087629     PISSN: 01788051     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00440-007-0106-x     Document Type: Article

References (26)

1. R. Bañuelos T. Kulczycki 2004 The Cauchy process and the Steklov problem J. Funct. Anal. 211 2 355 423
2. R. Bañuelos T. Kulczycki 2006 Eigenvalue gaps for the Cauchy process and a Poincare inequality J. Funct. Anal. 234 1 199 225
3. R. Bañuelos T. Kulczycki 2006 Spectral gap for the Cauchy process on convex, symmetric domains Comm. Partial Diff. Eq. 31 12 1841 1878
4. R. Bañuelos R. Latała P.J. Méndez-Hernández 2001 A Brascamp-Lieb-Luttinger-type inequality and applications to symmetric stable processes Proc. Am. Math. Soc. 129 10 2997 3008 (electronic)
5. M. van den Berg 1987 On the asymptotics of the heat equation and bounds on traces associated with Dirichlet Laplacian J. Funct. Anal. 71 279 293
6. R.M. Blumenthal R.K. Getoor 1959 The asymptotic distribution of the eigenvalues for a class of Markov operators Pac. J. Math. 9 399 408
7. R.M. Blumenthal R.K. Getoor D.B. Ray 1961 On the distribution of first hits for the symmetric stable processes Trans. Am. Math. Soc. 99 540 554
8. K. Bogdan 1997 The boundary Harnack principle for the fractional Laplacian Stud. Math. 123 43 80
9. J. Brossard R. Carmona 1986 Can one hear the dimension of a fractal? Comm. Math. Phys. 104 103 122
10. R.M. Brown 1993 The trace of the heat kernel in Lipschitz domains Trans. Am. Math. Soc. 339 889 900
11. Z.-Q. Chen R. Song 2006 Continuity of eigenvalues for subordinate processes in domains Math. Z. 252 71 89
12. Z.-Q. Chen R. Song 1998 Estimates on Green functions and Poisson kernels for symmetric stable processes Math. Ann. 312 465 501
13. Z.-Q. Chen R. Song 1997 Intrinsic ultracontractivity and conditional gauge for symmetric stable processes J. Funct. Anal. 150 204 239
14. Z.-Q. Chen R. Song 2005 Two-sided eigenvalue estimates for subordinate processes in domains J. Funct. Anal. 226 90 113
15. Davies E.B. (1989). Heat Kernels and Spectral Theory. Cambridge University Press, Cambridge
16. R.D. DeBlassie 2004 Higher order PDEs and symmetric stable processes Probab. Theory Relat. Fields 129 495 536
17. R.D. DeBlassie P.J. Méndez-Hernández 2007 α-continuity properties of the symmetric α-stable process Trans. Am. Math. Soc. 359 5 2343 2359
18. B. Dyda T. Kulczycki 2007 Spectral gap for stable process on convex planar double symmetric domains Potential Anal. 27 101 132
19. Feller W. (1971). An Introduction to Probability Theory and its Applications, vol. II. Wiley, New York
20. N. Ikeda S. Watanabe 1962 On some relations between the harmonic measure and the Levy measure for a certain class of Markov processes J. Math. Kyoto Univ. 2 79 95
21. T. Kulczycki 1997 Properties of Green function of symmetric stable processes Prob. Math. Stat. 17 2 339 364
22. T. Kulczycki B. Siudeja 2006 Intrinsic ultracontractivity of the Feynman-Kac semigroup for relativistic stable processes Trans. Am. Math. Soc. 358 5025 5057 (electronic)
23. Kwaśnicki, M.: Spectral gap estimate for fractional Laplacian (preprint)
24. P.J. Méndez-Hernández 2002 Brascamp-Lieb-Luttinger inequalities for convex domains of finite inradius Duke Math. J. 113 93 131
25. Simon, B.: Functional integration and quantum physics. In: Pure and Applied Mathematics, vol. 86. Academic [Harcourt Brace Jovanovich, Publishers], New York (1979)
26. Zolotarev, V.M.: Integral transformations of distributions and estimates of parameters of multidimensional spherically symmetric stable laws. In: Contributions to Probability. Academic, New York, pp. 283-305 (1981)