Radiation conditions and resolvent estimates for relativistic Schrödinger operators

 Access to full text

 Full (PDF)

1. [1] S. Agmon, Spectral properties of Schrödinger operators and scattering theory, Ann. Scoula Norm. Sup. Pisa (4), Vol. 2, 1975, pp. 151-218. Zbl0315.47007MR397194
2. [2] G. Arsu, Spectral analysis for simply characteristic operators by Mourre's methods. II, J. Operator Theory, Vol. 29, 1993, 287-305. Zbl0816.47007MR1284885
3. [3] E. Balslev and B. Helffer, Limiting absortption principle and resonances for the Dirac operator, Adv. Appl. Math., Vol. 13, 1992, pp. 186-215. Zbl0756.35062MR1162140
4. [4] R. Carmona, W.C. Masters and B. Simon, Relativistic Schrödinger operators: Asymptotic behavior of the eigenfunctions, J. Funct. Analysis, Vol. 91, 1990, pp. 117-142. Zbl0716.35006MR1054115
5. [5] I. Daubechies, One electron molecules with relativistic kinetic energy: Properties of the discrete spectrum, Commun. Math. Phys., Vol. 94, 1984, pp. 523-535. MR763750
6. [6] J Dereziński, The Mourre estimate for dispersive N-body Schrödinger operators, Trans. Amer. Math. Soc., Vol. 317, 1990, pp. 773-798. Zbl0691.47004MR970265
7. [7] C. Gérard, The Mourre estimate for regular dispersive systems, Ann. Inst. H. Poincaré, Phys. théor., Vol. 54, 1991, pp. 59-88. Zbl0724.35083MR1102972
8. [8] B. Helffer and B. Parisse, Comparaison entre la décroissance de fonctions propres pour les opérateurs de Dirac et de Klein-Gordon. Application à l'étude de l'effet tunnel, Ann. Inst. H.-Poincaré, Phys. théor., Vol. 60, 1994, pp. 147-187. Zbl0842.35088MR1270294
9. [9] I. Herbst, Spectral theory of the operator (p2 + m2)1/2 - Z e2/r, Commun. Math. Phys., Vol. 53, 1977, pp. 285-294. Zbl0375.35047MR436854
10. [10] T. Ikebe and Y. Saitō, Limiting absorption method and absolute continuity for the Schrödinger operators, J. Math. Kyoto Univ., Vol. 7, 1972, pp. 513-542. Zbl0257.35022MR312066
11. [11] H. Kumano-Go, Pseudo-differential operators, MIT Press, Cambridge, MA, 1981. 
12. [12] S.T. Kuroda, An introduction of scattering theory, Lecture Note Series No. 51, Aarhus Univ., 1978. Zbl0407.47003MR528757
13. [13] E.H. Lieb, The stability of matters: From atoms to stars, Bull. Amer. Math. Soc., Vol. 22, 1990, pp. 1-49. Zbl0698.35135MR1014510
14. [14] M. Murata, High energy resolvent estimates, I, first order operators, J. Math. Soc. Japan, Vol. 35, 1983, pp. 711-733. Zbl0513.35010MR714471
15. [15] M. Nagase and T. Umeda, On the essential self-adjointnes of pseudo-differential operators, Proc. Japan Acad., Vol. 64, Ser. A, 1988, pp. 94-97. Zbl0669.35115MR966395
16. [16] F. Nardini, Exponential decay for the eigenfunctions of the two-body relativistic Hamiltonian, J. d'Analyse Math., Vol. 47, 1986, pp. 87-109. Zbl0626.35075MR874046
17. [17] C. Pladdy, Y. Saitō and T. Umeda, Asymptotic behavior of the resolvent of the Dirac operator, in Operator Theory: Advances and Applications, Vol. 70, Mathematical Results in Quantum Mechanics, M. DEMUTH, P. EXNER, H. NEIDHARDT and V. ZAGREBNOV Eds., Birkhäuser, Basel, 1994. Zbl0879.47030MR1308997
18. [18] C. Pladdy, Y. Saitō and T. Umeda, Resolvent estimates of the Dirac operators, to appear in Analysis. Zbl0826.35090MR1344247
19. [19] C. Pladdy, Y. Saitō and T. Umeda, Radiation condition for Dirac operators, preprint. Zbl0928.35031MR1625972
20. [20] Y. Saitō, The principle of limiting absorption for the non-selfadjoint Schrödinger operator in RN (N ≠ 2), Publ. Res. Inst. Math. Sci. Kyoto Univ., Vol. 9, 1974, pp. 397-428. Zbl0287.35032MR477502
21. [21 ] Y. Saitō, The principle of limiting absorption for the non-selfadjoint Schrödinger operator in R2, Osaka J. Math., Vol. 11, 1974, pp. 295-306. Zbl0291.35019MR369954
22. [22] Y. Saitō, Some properties of the scattering amplitude and the inverse scattering problem, Osaka J. Math., Vol. 19, 1982, pp. 527-547. Zbl0498.35070MR676235
23. [23] Y. Saitō, An asymptotic behavior of the S-matrix and the inverse scattering problem, J. Math. Phys., Vol. 25, 1984, pp. 3105-3111. Zbl0557.35029MR760589
24. [24] T. Umeda, Scattering theory for pseudo-differential operators I. The existence of wave operators, Osaka J. Math., Vol. 18, 1981, pp. 361-392. Zbl0471.35066MR628839
25. [25] R. Weder, Spectral analysis of pseudodifferential operators, J. Funct. Analysis, Vol. 20, 1975, pp. 319-337. Zbl0317.47035MR402547
26. [26] R. Weder, Spectral properties of one-body relativistic spin-zero hamiltonians, Ann. Inst. H. Poincaré, Phys. théor., Vol. 20, 1974, pp. 211-220. MR351332
27. [27] O. Yamada, A remark on the limiting absorption method for Dirac operators, Proc. Japan Acad., Vol. 69, Ser. A, 1993, pp. 243-246. Zbl0831.35149MR1249220

1. Matania Ben-Artzi, Jonathan Nemirovsky, Remarks on relativistic Schrödinger operators and their extensions