Schrödinger operators with form-bounded potentials in L p -spaces
Annales de l'I.H.P. Physique théorique, Volume 52 (1990) no. 2, p. 151-161
@article{AIHPA_1990__52_2_151_0,
     author = {Perelmuter, M. A.},
     title = {Schr\"odinger operators with form-bounded potentials in $L^p$-spaces},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     publisher = {Gauthier-Villars},
     volume = {52},
     number = {2},
     year = {1990},
     pages = {151-161},
     zbl = {0744.35010},
     mrnumber = {1051234},
     language = {en},
     url = {http://www.numdam.org/item/AIHPA_1990__52_2_151_0}
}
Perelmuter, M. A. Schrödinger operators with form-bounded potentials in $L^p$-spaces. Annales de l'I.H.P. Physique théorique, Volume 52 (1990) no. 2, pp. 151-161. http://www.numdam.org/item/AIHPA_1990__52_2_151_0/

[1] A.Ya. Povzner, On the Expansions of Arbitrary Functions in Terms of Eigenfunctions of the Operator -Δu+Cu, Mat. Sbornik, Vol. 32, No. 1, 1953, pp. 109-156 ; A.M.S. Trans. Ser. 2, Vol. 60, 1967, pp. 1-49. | MR 53330 | Zbl 0179.14504

[2] M.A. Perelmuter, Positivity Preserving Operators and One Criterion of Essential Self-Adjointness, J. Math. Anal. Appl., Vol. 82, No. 2, 1981, pp. 406-419. | MR 629767 | Zbl 0482.47017

[3] Yu.A. Semenov, One Criterion of Essential Self-Adjointness of the Schrödinger Operator with Negative Potential, Kiev, preprint, 1987.

[4] V.F. Kovalenko, M.A. Perelmuter, Yu.A. Semenov, Schrödinger Operators with Ll/2w (Rl)-Potentials, J. Math. Phys., Vol. 22, No. 5, 1981, pp. 1033-1044. | MR 622855 | Zbl 0463.47027

[5] Yu.A. Semenov, On the Spectral Theory of Second-Order Elliptic Differential Operators, Math. U.S.S.R. Sbornik, Vol. 56, No. 1, 1987, pp. 221-247. | Zbl 0608.35046

[6] V.F. Kovalenko and Yu.A. Semenov, Lp-Contractivity of the Semigroup Generated by the Schrödinger Operator with Singular Negative Potential, Kiev, preprint, 1985.

[7] T. Kato, Lp-theory of Schrödinger Operators with a Singular Potential, in Aspects of Positivity Funct. Anal. Proc. Conf., Tübingen, 24-28 June 1985, Amsterdam e. a., 1986, pp. 41-48. | MR 859719 | Zbl 0627.47025

[8] W.P. Novinger, Mean Convergence in Lp Spaces, Proc. Am. Math. Soc., Vol. 34, No. 2, 1972, pp. 627-628. | MR 294595 | Zbl 0254.28011

[9] R.A. Adams, Sobolev Spaces, New York e. a., Academic Press, 1975. | MR 450957 | Zbl 0314.46030

[10] D. Kinderlehrer and G. Stampacchia, An Introduction to Variational Inequalities and Their Applications, New York e. a., Academic Press, 1980. | MR 567696 | Zbl 0457.35001

[11] M. Reed and B. Simon, Methods of Modern Mathematical Physics, New York, San Francisco, London, Academic Press, 1978.

[12] N. Th. Varopoulos, Hardy-Littlewood Theory for Semi-Groups, J. Funct. Anal., Vol. 63, No. 2, 1985, pp. 240-260. | MR 803094 | Zbl 0608.47047

[13] C.G. Simader, Essential Self-Adjointness of Schrödinger Operators Bounded from Below, Math. Z., Vol. 159, No. 1, 1978, pp. 47-50. | MR 470456 | Zbl 0409.35026

[14] H. Brezis, "Localized" Self-Adjointness of Schrödinder Operators, J. Oper. Theor., Vol. 1, No. 2, 1979, pp. 287-290. | Zbl 0439.35021

[15] M. Combescure-Moulin and J. Ginibre, Essential Self-Adjointness of Many-Particle Schrödinger Hamiltonians with Singular Twobody Potentials, Ann. Inst. H. Poincaré, Vol. A23, No. 3, 1975, p. 211-234. | Numdam | Zbl 0343.47007

[16] V.F. Kovalenko and Yu.A. Semenov, Essential Self-Adjointness of Many-Particle Hamiltonian Operators of Schrödinger Type with Singular Two-Particle Potentials, Ann. Inst. H. Poincaré, Vol. A24, No. 4, 1977, pp. 325-334. | Numdam | MR 441154

[17] E.H. Lieb and W.E. Thirring, Gravitational Collapse in Quantum Mechanics with Relativistic Kinetic Energy, Ann. Phys. (U.S.A.), Vol. 155, No. 2, 1984, pp. 494-512. | MR 753345

[18] C.J.K. Batty and E.B. Davies, Positive Semi-Groups and Resolvents, J. Oper. Theor., Vol. 10, No. 2, 1983, pp. 357-363. | MR 728915 | Zbl 0529.47026