Bounds on the eigenvalues of the Laplace and Schroedinger operators
HTML articles powered by AMS MathViewer
- by Elliott Lieb PDF
- Bull. Amer. Math. Soc. 82 (1976), 751-753
References
-
1. H. Weyl, Das asymptotische Verteilungsgesetz der Eigenwerte linearer partieller Differentialgleichungen, Math. Ann. 71 (1911), 441-469.
- Mark Kac, Can one hear the shape of a drum?, Amer. Math. Monthly 73 (1966), no. 4, 1–23. MR 201237, DOI 10.2307/2313748 3. S. Minakshisundaram and A. Pleijel, Some properties of the eigenfunctions of the Laplace-operator on Riemannian manifolds, Canad. J. Math 1 (1949), 242—256. MR 11, 108.
- Vojislav G. Avakumović, Über die Eigenfunktionen auf geschlossenen Riemannschen Mannigfaltigkeiten, Math. Z. 65 (1956), 327–344 (German). MR 80862, DOI 10.1007/BF01473886
- Lars Hörmander, The spectral function of an elliptic operator, Acta Math. 121 (1968), 193–218. MR 609014, DOI 10.1007/BF02391913 6. A. Martin, Bound states in the strong coupling limit, Helv. Phys. Acta 45 (1972), 140-148.
- Hideo Tamura, The asymptotic eigenvalue distribution for non-smooth elliptic operators, Proc. Japan Acad. 50 (1974), 19–22. MR 364899 8. M. Š. Birman and V. V. Borzov, On the asymptotic formula for the discrete spectrum of certain singular differential operators, Problemy Mat. Fiz., vyp. 5, Izdat. Leningrad. Gos Univ. Leningrad, 1971, pp. 24—38 = Topics in Math. Phys., no. 5, Plenum Press, New York, 1972, pp. 19—30; Consultants Bureau Transl., pp. 1-18. MR 46 #726.
- Michael Cwikel, Weak type estimates for singular values and the number of bound states of Schrödinger operators, Ann. of Math. (2) 106 (1977), no. 1, 93–100. MR 473576, DOI 10.2307/1971160
- Barry Simon, Analysis with weak trace ideals and the number of bound states of Schrödinger operators, Trans. Amer. Math. Soc. 224 (1976), no. 2, 367–380. MR 423128, DOI 10.1090/S0002-9947-1976-0423128-X
Additional Information
- Journal: Bull. Amer. Math. Soc. 82 (1976), 751-753
- MSC (1970): Primary 58G99, 35J05, 35J10, 35P15, 35P20; Secondary 47F05, 81A09, 81A45
- DOI: https://doi.org/10.1090/S0002-9904-1976-14149-3
- MathSciNet review: 0407909