@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},
pages = {265--297},
year = {1989},
publisher = {Gauthier-Villars},
volume = {51},
number = {3},
mrnumber = {1034589},
zbl = {0721.35059},
language = {en},
url = {https://www.numdam.org/item/AIHPA_1989__51_3_265_0/}
}
TY - JOUR AU - Ichinose, Takashi TI - Essential selfadjointness of the Weyl quantized relativistic hamiltonian JO - Annales de l'I.H.P. Physique théorique PY - 1989 SP - 265 EP - 297 VL - 51 IS - 3 PB - Gauthier-Villars UR - https://www.numdam.org/item/AIHPA_1989__51_3_265_0/ LA - en ID - AIHPA_1989__51_3_265_0 ER -
Ichinose, Takashi. Essential selfadjointness of the Weyl quantized relativistic hamiltonian. Annales de l'I.H.P. Physique théorique, Tome 51 (1989) no. 3, pp. 265-297. https://www.numdam.org/item/AIHPA_1989__51_3_265_0/
[1] and , Symbols of Operators and Quantization, Coll. Math. Soc. Janos Bolyai 5, Hilbert Space Operators, 21-52, Tihany, 1970. | Zbl | MR
[2] , One-Electron Molecules with Relativistic Kinetic Energy: Properties of the Discrete Spectrum, Commun. Math. Phys., Vol. 94, 1984, pp. 523-535. | MR
[3] and , One Electron Relativistic Molecules with Coulomb Interaction, Commun. Math. Phys., Vol. 90, 1983, pp. 497-510. | Zbl | MR
[4] , Higher Transcendental Functions, Vol. 2, McGraw-Hill, New York, 1953. | Zbl
[5] and , Relativistic Stability of Matter-I, Rev. Mat. Iberoamericana, Vol. 2, 1986, pp. 119-213. | Zbl | MR
[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. | Zbl | MR
[7] , and , Domination of Semigroups and Generalization of Kato's Inequality, Duke Math. J., Vol. 44, 1977, pp. 893-904. | Zbl | MR
[8] , The Analysis of Linear Partial Differential Operators III, Springer, Berlin-Heidelberg-New York-Tokyo, 1985. | Zbl | MR
[9] , The Nonrelativistic Limit Problem for a Relativistic Spinless Particle in an Electromagnetic Field, J. Functional Analysis, 73, 1987, pp. 233-257. | Zbl | MR
[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. | Zbl | MR
[11] , Kato's Inequality and Essential Selfadjointness for the Weyl Quantized Relativistic Hamiltonian, Proc. Japan Acad., 64A, 1988, pp. 367-369. | Zbl | MR
[12] and , 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. | Zbl | MR
[13] and , Uniqueness of the Self-Adjoint Extension of Singular Elliptic Differential Operators, Arch. Rat. Mech. Anal., Vol. 9, 1962, pp. 77-92. | Zbl | MR
[14] and , Stochastic Differential Equations and Diffusion Processes, North-Holland/Kodansha, Amsterdam, Tokyo, 1981. | Zbl | MR
[15] and , 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. | Zbl | MR
[16] , Schrödinger Operators with Singular Potentials, Israel J. Math., Vol. 13, 1972, pp. 135-148. | Zbl | MR
[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
[19] , The Lp-Boundedness of Pseudo-Differential Operators with Non-Regular Symbols, Comm. in P.D.E., Vol. 2, 1977, pp. 1045-1061. | Zbl | MR
[20] and , 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. | Zbl | MR
[21] and , Methods of Modern Mathematical Physics, IV: Analysis of Operators, Academic Press, New York, 1975. | Zbl | MR
[22] , Pseudodifferential Operators and Spectral Theory. Springer, Berlin- Heidelberg, 1987. | Zbl | MR
[23] , An Abstract Kato's Inequality for Generators of Positivity Preserving Semi-groups, Indiana Univ. Math. J., Vol. 26, 1977, pp. 1067-1073. | Zbl | MR
[24] , Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, Princeton, 1970. | Zbl | MR
[25] , Spectral Analysis of Pseudodifferential Operators, J. Functional Analysis, 20, 1975, pp. 319-337. | Zbl | MR





