@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}, pages = {277--296}, publisher = {Gauthier-Villars}, volume = {63}, number = {3}, year = {1995}, mrnumber = {1363536}, zbl = {0844.47030}, language = {en}, url = {http://www.numdam.org/item/AIHPA_1995__63_3_277_0/} }
TY - JOUR AU - Umeda, Tomio TI - Radiation conditions and resolvent estimates for relativistic Schrödinger operators JO - Annales de l'I.H.P. Physique théorique PY - 1995 SP - 277 EP - 296 VL - 63 IS - 3 PB - Gauthier-Villars UR - http://www.numdam.org/item/AIHPA_1995__63_3_277_0/ LA - en ID - AIHPA_1995__63_3_277_0 ER -
Umeda, Tomio. Radiation conditions and resolvent estimates for relativistic Schrödinger operators. Annales de l'I.H.P. Physique théorique, Tome 63 (1995) no. 3, pp. 277-296. http://www.numdam.org/item/AIHPA_1995__63_3_277_0/
[1] Spectral properties of Schrödinger operators and scattering theory, Ann. Scoula Norm. Sup. Pisa (4), Vol. 2, 1975, pp. 151-218. | Numdam | MR | Zbl
,[2] Spectral analysis for simply characteristic operators by Mourre's methods. II, J. Operator Theory, Vol. 29, 1993, 287-305. | MR | Zbl
,[3] Limiting absortption principle and resonances for the Dirac operator, Adv. Appl. Math., Vol. 13, 1992, pp. 186-215. | MR | Zbl
and ,[4] Relativistic Schrödinger operators: Asymptotic behavior of the eigenfunctions, J. Funct. Analysis, Vol. 91, 1990, pp. 117-142. | MR | Zbl
, and ,[5] One electron molecules with relativistic kinetic energy: Properties of the discrete spectrum, Commun. Math. Phys., Vol. 94, 1984, pp. 523-535. | MR
,[6] The Mourre estimate for dispersive N-body Schrödinger operators, Trans. Amer. Math. Soc., Vol. 317, 1990, pp. 773-798. | MR | Zbl
,[7] The Mourre estimate for regular dispersive systems, Ann. Inst. H. Poincaré, Phys. théor., Vol. 54, 1991, pp. 59-88. | Numdam | MR | Zbl
,[8] 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 | Zbl
and ,[9] Spectral theory of the operator (p2 + m2)1/2 - Z e2/r, Commun. Math. Phys., Vol. 53, 1977, pp. 285-294. | MR | Zbl
,[10] Limiting absorption method and absolute continuity for the Schrödinger operators, J. Math. Kyoto Univ., Vol. 7, 1972, pp. 513-542. | MR | Zbl
and ,[11] Pseudo-differential operators, MIT Press, Cambridge, MA, 1981.
,[12] An introduction of scattering theory, Lecture Note Series No. 51, Aarhus Univ., 1978. | MR | Zbl
,[13] The stability of matters: From atoms to stars, Bull. Amer. Math. Soc., Vol. 22, 1990, pp. 1-49. | MR | Zbl
,[14] High energy resolvent estimates, I, first order operators, J. Math. Soc. Japan, Vol. 35, 1983, pp. 711-733. | MR | Zbl
,[15] On the essential self-adjointnes of pseudo-differential operators, Proc. Japan Acad., Vol. 64, Ser. A, 1988, pp. 94-97. | MR | Zbl
and ,[16] Exponential decay for the eigenfunctions of the two-body relativistic Hamiltonian, J. d'Analyse Math., Vol. 47, 1986, pp. 87-109. | MR | Zbl
,[17] 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 | Zbl
, and ,[18] Resolvent estimates of the Dirac operators, to appear in Analysis. | MR | Zbl
, and ,[19] Radiation condition for Dirac operators, preprint. | MR
, and ,[20] 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 | Zbl
,[21 ] The principle of limiting absorption for the non-selfadjoint Schrödinger operator in R2, Osaka J. Math., Vol. 11, 1974, pp. 295-306. | MR | Zbl
,[22] Some properties of the scattering amplitude and the inverse scattering problem, Osaka J. Math., Vol. 19, 1982, pp. 527-547. | MR | Zbl
,[23] An asymptotic behavior of the S-matrix and the inverse scattering problem, J. Math. Phys., Vol. 25, 1984, pp. 3105-3111. | MR | Zbl
,[24] Scattering theory for pseudo-differential operators I. The existence of wave operators, Osaka J. Math., Vol. 18, 1981, pp. 361-392. | MR | Zbl
,[25] Spectral analysis of pseudodifferential operators, J. Funct. Analysis, Vol. 20, 1975, pp. 319-337. | MR | Zbl
,[26] Spectral properties of one-body relativistic spin-zero hamiltonians, Ann. Inst. H. Poincaré, Phys. théor., Vol. 20, 1974, pp. 211-220. | Numdam | MR
,[27] A remark on the limiting absorption method for Dirac operators, Proc. Japan Acad., Vol. 69, Ser. A, 1993, pp. 243-246. | MR | Zbl
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