Quasi-classical asymptotics of local Riesz means for the Schrödinger operator in a moderate magnetic field

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1. [1] W.O. Amrein, A.-M. Boutet de Monvel-Berthier and V. Georgescu, Notes on The N-Body Problem, Part II, University of Geneve, preprint, Geneve, 1991. MR991005
2. [2] J. Avron, I. Herbst and B. Simon, Schrödinger operators with magnetic fields, I., Duke Math. J., Vol. 45 (4), 1978, pp. 847-883. Zbl0399.35029MR518109
3. [3] C.L. Fefferman, V.J. Ivrii, L.A. Seco and I.M. Sigal, The energy asymptotics of large Coulomb systems, Lecture Notes in Physics, Vol. 403 (E. Balslev, ed.), Springer, Heidelberg, pp. 79-99. Zbl0834.47066MR1181242
4. [4] B. Helffer and D. Robert, Calcul fonctionnel par la transformation de Mellin et opérateurs admissibles, J. Funct. Anal., Vol. 53, 1983, pp. 246-268. Zbl0524.35103MR724029
5. [5] L. Hörmander, The Analysis of Linear Partial Differential Operators, I, Springer, Berlin, 1983. Zbl0521.35001MR705278
6. [6] V. Ivrii and I.M. Sigal, Asymptotics of the ground state energies of Large Coulomb systems, Ann. of Math., Vol. 138, 1993, pp. 243-335. Zbl0789.35135MR1240575
7. [7] V. Ivrii, Semiclassical Microlocal Analysis and Precise Spectral Asymptotics, École Polytechnique, Preprints, Palaiseau, 1991-1992. 
8. [8] V. Ivrii, Estimates for the number of negative eigenvalues of the Schrödinger operator with a strong magnetic field, Soviet Math. Dokl., Vol. 36 (3), 1988, pp. 561-564. Zbl0661.35066MR936071
9. [9] V. Ivrii, Estimates for the number of negative eigenvalues of the Schrödinger operator with singular potentials, Proc. Int. Congr. Math. Berkeley, 1986, pp. 1084-1093. Zbl0719.47031MR922080
10. [10] L.D. Landau and E.M. Lifschitz, Quantum Mechanics - Nonrelativistic Theory, Pergamon Press, New York, 1965. Zbl0178.57901
11. [11] E.H. Lieb and B. Simon, The Thomas-Fermi theory of atoms, molecules and solids, Adv. in Math., Vol. 23, 1977, pp. 22-116. Zbl0938.81568MR428944
12. [12] E.H. Lieb, J.P. Solovej and J. Yngvason, Heavy atoms in the strong magnetic field of a neutron star, Phys. Rev. Letters, Vol. 69, 1992, pp. 749-752. 
13. [13] E.H. Lieb, J.P. Solovej and J. Yngvason, Asymptotics of heavy atoms in high magnetic fields: I. Lowest Landau band regions, Comm. Pure and Appl. Math. (to appear). Zbl0800.49041MR1272387
14. [14] E.H. Lieb, J.P. Solovej and J. Yngvason, Asymptotics of heavy atoms in high magnetic fields: II. Semiclassical regions, Comm. Math. Phys., Vol. 161, 1994, pp. 77-124. Zbl0807.47058MR1266071
15. [15] M. Reed and B. Simon, Methods of Modern Mathematical Physics, Vol. III, Academic Press, New York, 1979. Zbl0405.47007
16. [16] D. Robert, Autour de l'Approximation Semiclassique, Birkhäuser, Boston, 1987. Zbl0621.35001
17. [17] B. Simon, Lectures on Trace Ideals Methods, Cambridge University Press, London, 1979. MR541149
18. [18] A. Sobolev, The quasi-classical asymptotics of local Riesz means for the Schrödinger operator in a strong homogeneous magnetic field, Duke Math. J., Vol. 74 (2), 1994, pp. 319-429. Zbl0824.35151MR1272980
19. [19] A. Sobolev, The sum of eigenvalues for the Schrödinger operator with Coulomb singularities in a homogeneous magnetic field, University of Nantes Preprint, 1993. 

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