On combinatorics of schrödinger perturbations

Potential Analysis

Volumn 31, Issue 1, 2009, Pages 45-55

  Jakubowski, Tomasz ^a,b  

^a UNIVERSITÉ D'ANGERS   (France)

^b WROCLAW UNIVERSITY OF TECHNOLOGY   (Poland)

Author keywords

Schr dinger perturbations; Stirling numbers; Transition density

Indexed keywords

EID: 67349121284     PISSN: 09262601     EISSN: 1572929X     Source Type: Journal    
DOI: 10.1007/s11118-009-9123-y     Document Type: Article

References (24)

1. V Adamchik 1997 On Stirling numbers and Euler sums J. Comput. Appl. Math. 79 1 119 130 (Pubitemid 127424717)
2. K Bogdan T Byczkowski 2000 Potential theory of Schrödinger operator based on fractional laplacian Probab. Math. Stat. 20 2 293 335 (Pubitemid 33313655)
3. K Bogdan W Hansen T Jakubowski 2008 Time-dependent Schrödinger perturbations of transition densities Stud. Math. 189 3 235 254
4. K Bogdan T Jakubowski 2007 Estimates of heat kernel of fractional Laplacian perturbed by gradient operators Commun. Math. Phys. 271 1 179 198
5. K Bogdan P Sztonyk 2007 Estimates of the potential kernel and Harnack's inequality for the anisotropic fractional Laplacian Stud. Math. 181 2 101 123
6. B Böttcher 2008 Construction of time-inhomogeneous Markov processes via evolution equations using pseudo-differential operators J. Lond. Math. Soc. 78 605 621
7. D Branson 2000 Stirling numbers and Bell numbers: their role in combinatorics and probability Math. Sci. 25 1 1 31
8. Z-Q Chen R Song 2002 General gauge and conditional gauge theorems Ann. Probab. 30 3 1313 1339
9. G-S Cheon MEA El-Mikkawy H-G Seol 2006 New identities for Stirling numbers via Riordan arrays J. Korea Soc. Math. Educ. Ser. B Pure Appl. Math. 13 4 311 318
10. Erdélyi, A., Magnus, W., Oberhettinger, F., Tricomi, F.G.: Higher Transcendental Functions, vol. I. Robert E. Krieger, Melbourne (1981) (Based on notes left by Harry Bateman, With a preface by Mina Rees, with a foreword by E. C. Watson, Reprint of the 1953 original)
11. KP Evans N Jacob 2007 Feller semigroups obtained by variable order subordination Rev. Mat. Complut. 20 2 293 307
12. Graham, R.L., Knuth, D.E., Patashnik, O.: Concrete mathematics, 2nd edn. In: A foundation for Computer Science. Addison-Wesley, Reading (1994)
13. T Grzywny M Ryznar 2008 Two-sided optimal bounds for Green functions of half-spaces for relativistic α-stable process Potential Anal. 28 3 201 239
14. A Gulisashvili 2008 Classes of time-dependent measures, non-homogeneous Markov processes, and Feynman-Kac propagators Trans. Am. Math. Soc. 360 8 4063 4098
15. Gulisashvili, A., van Casteren, J.A.: Non-autonomous Kato Classes and Feynman-Kac Propagators. World Scientific, Hackensack (2006)
16. W Hansen 2006 Global comparison of perturbed Green functions Math. Ann. 334 3 643 678 (Pubitemid 43234672)
17. T Jakubowski 2002 The estimates for the Green function in Lipschitz domains for the symmetric stable processes Probab. Math. Stat. 22 2 419 441 (Pubitemid 36669333)
18. P Kim R Song 2007 Estimates on Green functions and Schrödinger-type equations for non-symmetric diffusions with measure-valued drifts J. Math. Anal. Appl. 332 1 57 80
19. T Kulczycki 1997 Properties of Green function of symmetric stable processes Probab. Math. Stat. 17 2 339 364 (Pubitemid 128087871)
20. W Liang 2006 An identity of Stirling numbers of the second kind Sci. Mag. 2 2 40 43
21. V Liskevich H Vogt J Voigt 2006 Gaussian bounds for propagators perturbed by potentials J. Funct. Anal. 238 1 245 277 (Pubitemid 44057688)
22. A Stós 2000 Symmetric α-stable processes on d-sets Bull. Pol. Acad. Sci. Math. 48 3 237 245
23. P Sun 2005 Product of uniform distribution and Stirling numbers of the first kind Acta Math. Sin. Engl. Ser. 21 6 1435 1442 (Pubitemid 41698128)
24. Tanabe, H.: Equations of evolution. In: Monographs and Studies in Mathematics, vol. 6. Pitman (Advanced Publishing Program), Boston (1979) (Translated from the Japanese by N. Mugibayashi and H. Haneda)