On Schrödinger semigroups and related topics

Journal of Functional Analysis

Volumn 256, Issue 6, 2009, Pages 1998-2025

  Mokhtar Kharroubi, Mustapha ^a  

^a UNIVERSITÉ DE FRANCHE COMTÉ   (France)

Author keywords

Essential self adjointness; Form perturbation; Kato class; Positive semigroups; Schr dinger operator; Weak compactness

Indexed keywords

EID: 59849122064     PISSN: 00221236     EISSN: 10960783     Source Type: Journal    
DOI: 10.1016/j.jfa.2008.11.012     Document Type: Article

References (45)

1. Aizenman M., and Simon B. Brownian motion and Harnack inequality for Schrödinger operators. Comm. Pure Appl. Math. 35 (1982) 209-273
2. Aliprantis C.D., and Burkinshaw O. Positive Operators (1985), Academic Press, New York
3. Arendt W., and Batty C.J.K. Absorption semigroups and Dirichlet boundary conditions. Math. Ann. 295 (1993) 427-448
4. Arendt W., and Rhandi A. Perturbation of positive semigroups. Arch. Math. 56 (1991) 107-119
5. Banasiak J., and Arlotti L. Perturbations of Positive Semigroups with Applications. Springer Monogr. Math. (2006), Springer, London
6. Batty C.J.K., and Robinson D.W. Positive one-parameter semigroups on ordered Banach spaces. Acta Appl. Math. 1 (1984) 221-296
7. Brezis H. Analyse fonctionnelle. Théorie et applications (1983), Masson, Paris
8. Brezis H., and Kato T. Remarks on the Schrödinger operator with singular complex potentials. J. Math. Pures Appl. 58 9 (1979) 137-151
9. Carmona R. Regularity properties of Schrödinger and Dirichlet semigroups. J. Funct. Anal. 33 (1979) 259-296
10. 1 analyticity. J. London Math. Soc. 52 2 (1994) 177-184
11. Davies E.B., and Hinz A.M. Kato class potentials for higher order elliptic operators. J. London Math. Soc. 58 2 (1998) 669-678
12. 1-properties of intrinsic Schrödinger semigroups. J. Funct. Anal. 65 (1986) 126-146
13. W. Desch, Perturbations of positive semigroups in AL-spaces, unpublished manuscript, 1988
14. Devinatz A. Schrödinger operators with singular potentials. J. Operator Theory 4 (1980) 25-35
15. Dunford N., and Schwartz J.T. Linear Operators, Part I: General Theory (1958), Interscience, New York
16. Faris W.G. Essential self-adjointness of operators in ordered Hilbert spaces. Comm. Math. Phys. 30 (1973) 23-34
17. N). Trans. Amer. Math. Soc. 236 (1978) 325-360
18. Kato T. Schrödinger operators with singular potentials. Israel J. Math. 13 (1973) 135-148
19. Kato T. A second look at the essential self-adjointness of Schrödinger operators. In: Enz C.P., and Mehra J. (Eds). Physical Reality and Mathematical Description (1974), Reidel Publishing Company, Dordrecht-Holland 193-201
20. Kato T. Perturbation Theory for Linear Operators (1976), Springer
21. p-theory of Schrödinger operators with a singular potential. In: Nagel R., Schlotterbeck U., and Wolf M.P.H. (Eds). Aspects of Positivity in Functional Analysis (1986), Mathematics Studies, North-Holland 63-78
22. McKean H.P. -Δ plus a bad potential. J. Math. Phys. 18 6 (1977) 1277-1279
23. l)-potentials. J. Math. Phys. 22 5 (1981) 1033-1044
24. Kovalenko V.F., and Semenov Yu.A. Some problems on expansion in generalized eigenfunctions of the Schrödinger operator with strongly singular potentials. Russian Math. Surveys 33 (1978) 119-157
25. Kovalenko V.F., and Semenov Yu.A. Towards the theory of Schrödinger operators I. translation from. Ukrain. Mat. Zh. 41 2 (1989) 273-278
26. Liskevich V.A., and Semenov Yu.A. Some problems on Markov semigroups. In: Demuth M., Schrohe E., Schulze B., and Sjöstrand J. (Eds). Schrödinger Operators, Markov Semigroups, Wavelet Analysis, Operator Algebras (1996), Akademie, Berlin 163-217
27. Mokhtar-Kharroubi M. Mathematical Topics in Neutron Transport Theory. New Aspects. Ser. Adv. Math. Appl. Sci. vol. 46 (1997), World Scientific
28. M. Mokhtar-Kharroubi, On resolvent positive operators in ordered Banach spaces with additive norm and application to semigroup theory, Prépublication du Laboratoire de Mathématiques de Besançon, No. 36, 2007
29. M. Mokhtar-Kharroubi, On perturbation theory of holomorphic semigroups, Extension of Kato class potentials for higher order elliptic operators and for Schrödinger operators with magnetic fields, in preparation
30. p theory for Schrödinger operators with nonnegative potentials. J. Math. Soc. Japan 36 4 (1984) 675-688
31. Ouhabaz E.M. Gaussian estimates and holomorphy of semigroups. Proc. Amer. Math. Soc. 123 5 (1995) 1465-1474
32. de Pagter B. Ordered Banach spaces. In: Clément Ph., Heijmans H.J.A.M., Angenent S., van Duijn C.J., and de Pagter B. (Eds). One-Parameter Semigroups (1987), North-Holland, Amsterdam 269-279
33. Reed M., and Simon B. Methods of Modern Mathematical Physics, vol. II (1975), Academic Press
34. A. Rhandi, Perturbations positives des équations d'évolution et applications, PhD thesis, Besançon University, 1990
35. Schechter M. Spectra of Partial Differential Operators (1971), North-Holland
36. Schechter M. Hamiltonians for singular potentials. Indiana Univ. Math. J. 22 5 (1972) 483-503
37. p-potentials. Comm. Math. Phys. 53 (1977) 277-284
38. Simon B. Essential sef-adjointness of Schrödinger operators with positive potentials. Math. Ann. 201 (1973) 211-220
39. Simon B. Maximal and minimal Schrödinger forms. J. Operator Theory 1 (1979) 37-47
40. Simon B. Schrödinger semigroups. Bull. Amer. Math. Soc. 7 3 (1982) 447-526
41. Simon B. Schrödinger operators in the twentieth century. J. Math. Phys. 41 6 (2000) 3523-3555
42. Trudinger N.S. Linear elliptic operators with measurable coefficients. Ann. Sc. Norm. Super. Pisa Cl. Sci. 27 3 (1973) 265-308
43. Voigt J. Absorption semigroups, their generators, and Schrödinger semigroups. J. Funct. Anal. 67 (1986) 167-205
44. Yosida K. Functional Analysis (1978), Springer
45. Ziemer W.P. Weakly Differentiable Functions (1989), Springer-Verlag