Radiation conditions and resolvent estimates for relativistic Schrödinger operators
Umeda, Tomio
Annales de l'I.H.P. Physique théorique, Tome 63 (1995), p. 277-296 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@article{AIHPA_1995__63_3_277_0,
     author = {Umeda, Tomio},
     title = {Radiation conditions and resolvent estimates for relativistic Schr\"odinger operators},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     volume = {63},
     year = {1995},
     pages = {277-296},
     mrnumber = {1363536},
     zbl = {0844.47030},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPA_1995__63_3_277_0}
}

Umeda, Tomio. Radiation conditions and resolvent estimates for relativistic Schrödinger operators. Annales de l'I.H.P. Physique théorique, Tome 63 (1995) pp. 277-296. http://gdmltest.u-ga.fr/item/AIHPA_1995__63_3_277_0/

[1] S. Agmon, Spectral properties of Schrödinger operators and scattering theory, Ann. Scoula Norm. Sup. Pisa (4), Vol. 2, 1975, pp. 151-218. | Numdam | MR 397194 | Zbl 0315.47007

[2] G. Arsu, Spectral analysis for simply characteristic operators by Mourre's methods. II, J. Operator Theory, Vol. 29, 1993, 287-305. | MR 1284885 | Zbl 0816.47007

[3] E. Balslev and B. Helffer, Limiting absortption principle and resonances for the Dirac operator, Adv. Appl. Math., Vol. 13, 1992, pp. 186-215. | MR 1162140 | Zbl 0756.35062

[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. | MR 1054115 | Zbl 0716.35006

[5] I. Daubechies, One electron molecules with relativistic kinetic energy: Properties of the discrete spectrum, Commun. Math. Phys., Vol. 94, 1984, pp. 523-535. | MR 763750

[6] J Dereziński, The Mourre estimate for dispersive N-body Schrödinger operators, Trans. Amer. Math. Soc., Vol. 317, 1990, pp. 773-798. | MR 970265 | Zbl 0691.47004

[7] C. Gérard, The Mourre estimate for regular dispersive systems, Ann. Inst. H. Poincaré, Phys. théor., Vol. 54, 1991, pp. 59-88. | Numdam | MR 1102972 | Zbl 0724.35083

[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. | Numdam | MR 1270294 | Zbl 0842.35088

[9] I. Herbst, Spectral theory of the operator (p2 + m2)1/2 - Z e2/r, Commun. Math. Phys., Vol. 53, 1977, pp. 285-294. | MR 436854 | Zbl 0375.35047

[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. | MR 312066 | Zbl 0257.35022

[11] H. Kumano-Go, Pseudo-differential operators, MIT Press, Cambridge, MA, 1981.

[12] S.T. Kuroda, An introduction of scattering theory, Lecture Note Series No. 51, Aarhus Univ., 1978. | MR 528757 | Zbl 0407.47003

[13] E.H. Lieb, The stability of matters: From atoms to stars, Bull. Amer. Math. Soc., Vol. 22, 1990, pp. 1-49. | MR 1014510 | Zbl 0698.35135

[14] M. Murata, High energy resolvent estimates, I, first order operators, J. Math. Soc. Japan, Vol. 35, 1983, pp. 711-733. | MR 714471 | Zbl 0513.35010

[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. | MR 966395 | Zbl 0669.35115

[16] F. Nardini, Exponential decay for the eigenfunctions of the two-body relativistic Hamiltonian, J. d'Analyse Math., Vol. 47, 1986, pp. 87-109. | MR 874046 | Zbl 0626.35075

[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. | MR 1308997 | Zbl 0879.47030

[18] C. Pladdy, Y. Saitō and T. Umeda, Resolvent estimates of the Dirac operators, to appear in Analysis. | MR 1344247 | Zbl 0826.35090

[19] C. Pladdy, Y. Saitō and T. Umeda, Radiation condition for Dirac operators, preprint. | MR 1625972

[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. | MR 477502 | Zbl 0287.35032

[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. | MR 369954 | Zbl 0291.35019

[22] Y. Saitō, Some properties of the scattering amplitude and the inverse scattering problem, Osaka J. Math., Vol. 19, 1982, pp. 527-547. | MR 676235 | Zbl 0498.35070

[23] Y. Saitō, An asymptotic behavior of the S-matrix and the inverse scattering problem, J. Math. Phys., Vol. 25, 1984, pp. 3105-3111. | MR 760589 | Zbl 0557.35029

[24] T. Umeda, Scattering theory for pseudo-differential operators I. The existence of wave operators, Osaka J. Math., Vol. 18, 1981, pp. 361-392. | MR 628839 | Zbl 0471.35066

[25] R. Weder, Spectral analysis of pseudodifferential operators, J. Funct. Analysis, Vol. 20, 1975, pp. 319-337. | MR 402547 | Zbl 0317.47035

[26] R. Weder, Spectral properties of one-body relativistic spin-zero hamiltonians, Ann. Inst. H. Poincaré, Phys. théor., Vol. 20, 1974, pp. 211-220. | Numdam | MR 351332

[27] O. Yamada, A remark on the limiting absorption method for Dirac operators, Proc. Japan Acad., Vol. 69, Ser. A, 1993, pp. 243-246. | MR 1249220 | Zbl 0831.35149