Commutators, C0-semigroups and resolvent estimates

Journal of Functional Analysis

Volumn 216, Issue 2, 2004, Pages 303-361

  Georgescu, Vladimir ^a   Gérard, Christian ^b   Møller, Jacob S ^c  

^a UNIVERSITÉ DE CERGY PONTOISE   (France)

^b Université Paris Sud   (France)

^c JOHANNES GUTENBERG UNIVERSITY   (Germany)

Author keywords

Boundary values of resolvent families; C0 semigroups; Conjugate operator; Mourre estimate; Positive commutators; Resolvent estimates; Virial theorem

Indexed keywords

EID: 4344663368     PISSN: 00221236     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jfa.2004.03.004     Document Type: Article

References (33)

1. Agmon S. Herbst I. Skibsted E. Perturbation of embedded eigenvalues in the generalized N-body problem Comm. Math. Phys. 122 1989 411-438
2. S. Agmon, I. Herbst, S. Maad, in preparation.
3. Ammari Z. Asymptotic completeness for a renormalized non-relativistic Hamiltonian in quantum field theory: the Nelson model Math. Phys. Anal. Geom. 3 2000 217-285
4. 0-Groups, Commutator Methods and Spectral Theory of N-body Hamiltonians 1996 Birkhäuser Basel-Boston-Berlin
5. Bach V. Fröhlich J. Sigal I.M. Soffer A. Positive commutators and the spectrum of Pauli-Fierz Hamiltonian of atoms and molecules Comm. Math. Phys. 207 1999 557-587
6. Bennett C. Sharpley R. Interpolation of Operators 1988 Academic Press Boston
7. Boutet de Monvel A. Georgescu V. Limiting absorption principle for long-range perturbations of pseudodifferential operators In: Albeverio S. Figari R. Orlandi E. Teta A. (Eds.) Advances in Dynamical Systems and Quantum Physics 1994 World Scientific Singapore
8. A. Boutet de Monvel, V. Georgescu, J. Sahbani, Higher order estimates in the conjugate operator theory, preprint mpc 97-428, 1997.
9. O. Bratteli, D. Robinson, Operator Algebras and Quantum Statistical Mechanics, Vol. 1, Springer, Berlin, 1979.
10. Dereziński J. Gérard C. Asymptotic completeness in quantum field theory: massive Pauli-Fierz Hamiltonians Rev. Math. Phys. 11 1999 383-450
11. 2 Hamiltonians Comm. Math. Phys. 213 2000 39-125
12. Dereziński J. Jaksic V. Spectral theory of Pauli-Fierz operators J. Funct. Anal. 180 2001 243-327
13. J. Dieudonné, Elements d'analyse, Vol. 2, Gauthier-Villars, Paris, 1969.
14. J. Fröhlich, M. Merkli, Thermal ionization, preprint mpc 02-447, 2002.
15. Georgescu V. Gérard C. On the virial theorem in quantum mechanics Comm. Math. Phys. 208 1999 275-281
16. V. Georgescu, C. Gérard, J.S. Møller, Spectral theory of massless Pauli-Fierz models, Comm. Math. Phys. to appear.
17. Hartman Ph. Ordinary Differential Equations 1982 Birkhäuser Basel
18. B. Helffer, J. Sjöstrand, Equation de Schrödinger avec champ magnétique et equation de Harper, Lecture Notes in Physics, Vol. 345, Springer, Berlin, 1989, pp. 118-197.
19. Hille E. Phillips R.S. Functional Analysis and Semigroups 1957 American Mathematical Society Providence, RI
20. L. Hörmander, The Analysis of Linear Partial Differential Operators, Vol. 2, Springer, Berlin, 1983.
21. Hoshiro T. Mourre's method and smoothing properties of dispersive equations Comm. Math. Phys. 202 1999 255-265
22. Hübner M. Spohn H. Spectral properties of the spin-boson Hamiltonian Ann. Inst. H. Poincaré 62 1995 289-323
23. Jensen A. Propagation estimates for Schrödinger type operators Trans. Amer. Math. Soc. 291 1985 129-144
24. Merkli M. Positive commutators in non-equilibrium quantum statistical mechanics Comm. Math. Phys. 223 2001 327-362
25. J.S. Møller, E. Skibsted, Spectral theory of time-periodic many-body systems, Adv. in Math, to appear.
26. Mourre E. Absence of singular continuous spectrum for certain self-adjoint operators Comm. Math. Phys. 91 1981 391-408
27. Perry P. Sigal I.M. Simon B. Spectral analysis of N-body Schrödinger operators Ann. Math. 114 1981 519-567
28. Putnam C.R. On commutators and Jacobi matrices Proc. Amer. Math. Soc. 7 1956 1026-1030
29. Putnam C.R. Commutation Properties of Hilbert Space Operators and Related Topics 1967 Springer Berlin
30. M. Reed, B. Simon, Methods of Modern Mathematical Physics, Vols. 1-4, Academic Press, New York, 1972-1980.
31. Skibsted E. Smoothness of N-body scattering amplitudes Rev. Math. Phys. 4 1992 619-658
32. Skibsted E. Spectral analysis of N-body systems coupled to a bosonic system Rev. Math. Phys. 10 1998 989-1026
33. Triebel H. Interpolation Theory, Function Spaces, Differential Operators 1978 VEB Deutscher Verlag der Wissenschaften Berlin