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Bounds on the eigenvalues of the Laplace and Schroedinger operators
Author(s):
Elliott
Lieb
Journal:
Bull. Amer. Math. Soc.
82
(1976),
751-753.
MSC (1970):
Primary 58G99, 35J05, 35J10, 35P15, 35P20;
Secondary 47F05, 81A09, 81A45
MathSciNet review:
0407909
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Additional information
References:
- 1.
- H. Weyl, Das asymptotische Verteilungsgesetz der Eigenwerte linearer partieller Differentialgleichungen, Math. Ann. 71 (1911), 441-469.
- 2.
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- 3.
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- 4.
- V. G. Avakumović, Über die Eigenfunktionen auf geschlossenen Riemannschen Mannigfaltigkeiten, Math. Z. 65 (1956), 327-344. MR 18, 316. MR 80862
- 5.
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- 6.
- A. Martin, Bound states in the strong coupling limit, Helv. Phys. Acta 45 (1972), 140-148.
- 7.
- H. Tamura, The asymptotic eigenvalue distribution for non-smooth elliptic operators, Proc. Japan Acad. 50 (1974), 19-22. MR 51 #1153. 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.
- 9.
- M. Cwikel, Weak type estimates for singular values and the number of bound states of Schroedinger operators, Institute for Advanced Study, Princeton, N. J., 1976 (preprint). MR 473576
- 10.
- B. Simon, Analysis with weak trace ideals and the number of bound states of Schrödinger operators, Trans. Amer. Math. Soc. (to appear). MR 423128
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58G99, 35J05, 35J10, 35P15, 35P20, 47F05, 81A09, 81A45
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58G99, 35J05, 35J10, 35P15, 35P20, 47F05, 81A09, 81A45
Additional Information:
DOI:
10.1090/S0002-9904-1976-14149-3
PII:
S 0002-9904(1976)14149-3
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