@article{AIHPA_1989__51_3_265_0, author = {Ichinose, Takashi}, title = {Essential selfadjointness of the Weyl quantized relativistic hamiltonian}, journal = {Annales de l'I.H.P. Physique th\'eorique}, volume = {51}, year = {1989}, pages = {265-297}, mrnumber = {1034589}, zbl = {0721.35059}, language = {en}, url = {http://dml.mathdoc.fr/item/AIHPA_1989__51_3_265_0} }
Ichinose, Takashi. Essential selfadjointness of the Weyl quantized relativistic hamiltonian. Annales de l'I.H.P. Physique théorique, Tome 51 (1989) pp. 265-297. http://gdmltest.u-ga.fr/item/AIHPA_1989__51_3_265_0/
[1] Symbols of Operators and Quantization, Coll. Math. Soc. Janos Bolyai 5, Hilbert Space Operators, 21-52, Tihany, 1970. | MR 366281 | Zbl 0262.47036
and ,[2] One-Electron Molecules with Relativistic Kinetic Energy: Properties of the Discrete Spectrum, Commun. Math. Phys., Vol. 94, 1984, pp. 523-535. | MR 763750
,[3] One Electron Relativistic Molecules with Coulomb Interaction, Commun. Math. Phys., Vol. 90, 1983, pp. 497-510. | MR 719430 | Zbl 0946.81522
and ,[4] Higher Transcendental Functions, Vol. 2, McGraw-Hill, New York, 1953. | Zbl 0052.29502
,[5] Relativistic Stability of Matter-I, Rev. Mat. Iberoamericana, Vol. 2, 1986, pp. 119-213. | MR 864658 | Zbl 0602.58015
and ,[6] Spectral Theory of the Operator (p2+m2)1/2-Ze2/r. Commun. Math. Phys., Vol. 53, 1977, pp. 285-294; Errata, Ibid., Vol. 55, 1977, p. 316. | MR 436854 | Zbl 0375.35047
,[7] Domination of Semigroups and Generalization of Kato's Inequality, Duke Math. J., Vol. 44, 1977, pp. 893-904. | MR 458243 | Zbl 0379.47028
, and ,[8] The Analysis of Linear Partial Differential Operators III, Springer, Berlin-Heidelberg-New York-Tokyo, 1985. | MR 781536 | Zbl 0601.35001
,[9] The Nonrelativistic Limit Problem for a Relativistic Spinless Particle in an Electromagnetic Field, J. Functional Analysis, 73, 1987, pp. 233-257. | MR 899650 | Zbl 0618.46063
,[10] Path Integral for a Weyl Quantized Relativistic Hamiltonian and the Nonrelativistic Limit Problem, in Differential Equations and Mathematical Physics; Lecture Notes in Mathematics, Springer, No. 1285, 1987, pp. 205-210. | MR 921270 | Zbl 0623.34007
,[11] Kato's Inequality and Essential Selfadjointness for the Weyl Quantized Relativistic Hamiltonian, Proc. Japan Acad., 64A, 1988, pp. 367-369. | MR 979947 | Zbl 0705.35116
,[12] Imaginary-Time Path Integral for a Relativistic Spinless Particle in an Electromagnetic Field, Commun. Math. Phys., Vol. 105, 1986, pp. 239- 257 ; Path Integral for the Weyl Quantized Relativistic Hamiltonian, Proc. Japan Acad., Vol. 62A, 1986, pp. 91-93. | MR 849207 | Zbl 0606.60060
and ,[13] Uniqueness of the Self-Adjoint Extension of Singular Elliptic Differential Operators, Arch. Rat. Mech. Anal., Vol. 9, 1962, pp. 77-92. | MR 142894 | Zbl 0103.31801
and ,[14] Stochastic Differential Equations and Diffusion Processes, North-Holland/Kodansha, Amsterdam, Tokyo, 1981. | MR 637061 | Zbl 0495.60005
and ,[15] On Some Relations Between the Harmonic Measure and the Lévy Measure for a Certain Class of Markov Processes, J. Math. Kyoto Univ., Vol. 2, 1962, pp. 79-95. | MR 142153 | Zbl 0118.13401
and ,[16] Schrödinger Operators with Singular Potentials, Israel J. Math., Vol. 13, 1972, pp. 135-148. | MR 333833 | Zbl 0246.35025
,[17] Pseudo-Differential Operators, The M.I.T. Press, Cambridge, Massachusetts, 1981.
,[18] The Weyl Correspondence and Path Integrals, J. Math. Phys., Vol. 16, 1975, pp.2201-2206. | MR 391805
,[19] The Lp-Boundedness of Pseudo-Differential Operators with Non-Regular Symbols, Comm. in P.D.E., Vol. 2, 1977, pp. 1045-1061. | MR 470758 | Zbl 0397.35071
,[20] On the Essential Self-Adjointness of Quantum Hamiltonians of Relativistic Particles in Magnetic Fields, Sci. Rep. Col. Gen. Educ. Osaka Univ., Vol. 36, 1987, pp. 1-6. | MR 931756 | Zbl 0649.47038
and ,[21] Methods of Modern Mathematical Physics, IV: Analysis of Operators, Academic Press, New York, 1975. | MR 751959 | Zbl 0401.47001
and ,[22] Pseudodifferential Operators and Spectral Theory. Springer, Berlin- Heidelberg, 1987. | MR 883081 | Zbl 0616.47040
,[23] An Abstract Kato's Inequality for Generators of Positivity Preserving Semi-groups, Indiana Univ. Math. J., Vol. 26, 1977, pp. 1067-1073. | MR 461209 | Zbl 0389.47021
,[24] Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, Princeton, 1970. | MR 290095 | Zbl 0207.13501
,[25] Spectral Analysis of Pseudodifferential Operators, J. Functional Analysis, 20, 1975, pp. 319-337. | MR 402547 | Zbl 0317.47035
,