Recent results on Lieb-Thirring inequalities

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1. [1] Aizenman M. and Lieb E.H.: On semi-classical bounds for eigenvalues of Schrödinger operators. Phys. Lett. 66A, 427-429 (1978) MR81m:81020
2. [2] Benguria R and Loss M.: A simple proof of a theorem by Laptev and Weidl. Preprint (1999). Zbl0963.34077
3. [3] Berezin F.A.: Covariant and contravariant symbols of operators. [English Translation] Math. USSR, 6, 1117-1151 (1972) Zbl0259.47004MR50 #2996
4. [4] Birman M.S.: The spectrum of singular boundary problems. (Russian) Mat. Sb. (N.S.) 55 (97), 125-174 (1961). (English) Amer. Math. Soc. Transl. 53, 23-80 (1966) Zbl0174.42502MR26 #463
5. [5] Birman M. S. and Laptev A.: The negative discrete spectrum of a two-dimensional Schrödinger operator. Comm. Pure and Appl. Math., XLIX, 967-997 (1996) Zbl0864.35080MR97i:35131
6. [6] Blanchard Ph. and Stubbe J.: Bound states for Schrödinger Hamiltonians: Phase Space Methods and Applications. Rev. Math. Phys., 35, 504-547 (1996) Zbl0859.35101
7. [7] Buslaev V.S. and Faddeev L.D: Formulas for traces for a singular Sturm-Liouville differential operator. [English translation], Dokl. AN SSSR, 132, 451-454 (1960) Zbl0129.06501MR22 #11171
8. [8] Cwikel M.: Weak type estimates for singular values and the number of bound states of Schrödinger operators. Trans. AMS, 224, 93-100 (1977) Zbl0362.47006MR57 #13242
9. [9] De la Bretèche R.: Preuve de la conjecture de Lieb-Thirring dans le cas des potentiels quadratiques strictement convexes. Ann. Inst. H. Poincaré Phys. théor., 70, 369-380 (1999) Zbl0938.35148MR2000e:81035
10. [10] Egorov Yu. V. and Kontrat'ev V.A.: On spectral theory of elliptic operators. Operator Theory: Advances and Applications, 89, Birkhäuser Verlag, Basel, 1996. x+328 pp. Zbl0855.35001MR97m:35189
11. [11] Faddeev L.D. and Zakharov V.E.: Korteweg-de Vries equation: A completely integrable hamiltonian system. Func. Anal. Appl., 5, 18-27 (1971) Zbl0257.35074
12. [12] Glaser V., Grosse H. and Martin A.: Bounds on the number of eigenvalues of the Schrödinger operator. Commun. Math. Phys., 59, 197-212 (1978) Zbl0373.35050MR81a:35081
13. [13] Helffer B. and Robert D.: Riesz means of bounded states and semi-classical limit connected with a Lieb-Thirring conjecture I, II. I -Jour. Asymp. Anal., 3, 91-103 (1990), II — Ann. de l'Inst. H. Poincare, 53 (2), 139-147 (1990) Zbl0717.35062MR91h:35241
14. [14] Hundertmark D., Laptev A. and Weidl T.: New bounds on the Lieb-Thirring constants. to appear in Inventiones mathematicae. Zbl1074.35569
15. [15] Hundertmark D., Lieb E.H. and Thomas L.E.: A sharp bound for an eigenvalue moment of the one-dimensional Schrödinger operator. Adv. Theor. Math. Phys. 2, 719-731 (1998) Zbl0929.34076MR2000c:81062
16. [16] Laptev A.: Dirichlet and Neumann Eigenvalue Problems on Domains in Euclidean Spaces. J. Func. Anal., 151, 531-545 (1997) Zbl0892.35115MR99a:35027
17. [17] Laptev A.: On the Lieb-Thirring conjecture for a class of potentials. Operator Theory: Adv. and Appl., 110, 227-234 (1999) Zbl0938.35112MR2001c:35174
18. [18] Laptev A., Weidl T.: Sharp Lieb-Thirring inequalities in high dimensions. Acta Mathematica, 184, 87-111 (2000) Zbl1142.35531MR2001c:35173
19. [19] Li P. and Yau S.-T.: On the Schrödinger equation and the eigenvalue problem. Comm. Math. Phys., 88, 309-318 (1983) Zbl0554.35029MR84k:58225
20. [20] Lieb, E.H.: The number of bound states of one body Schrödinger operators and the Weyl problem. Bull. Amer. Math. Soc., 82, 751-753 (1976) Zbl0329.35018
21. [21] Lieb, E.H.: Lieb-Thirring Inequalities. Preprint mp-arc 00-132 (2000) 
22. [22] Lieb E.H. and Thirring, W.: Inequalities for the moments of the eigenvalues of the Schrödinger Hamiltonian and their relation to Sobolev inequalities. Studies in Math. Phys., Essays in Honor of Valentine Bargmann., Princeton, 269-303 (1976) Zbl0342.35044
23. [23] Netrusov Y. and Weidl T.: On Lieb-Thirring inequalities for higher order operators with critical and subcritical powers. Comm. Math. Phys., 182 (1), 355-370 (1996) Zbl0865.47033MR98d:47103
24. [24] Rozenblum, G.V.: Distribution of the discrete spectrum of singular differential operators. Dokl. AN SSSR, 202, 1012-1015 (1972), Izv. VUZov, Matematika, 1, 75-86 (1976) Zbl0249.35069MR45 #4216
25. [25] Ruelle D.: Large volume limit of the distribution of characteristic exponents in turbulence. Comm. Math. Phys., 87, 287-302 (1982) Zbl0546.76083MR85c:76046
26. [26] Y.Schwinger: On the bound states for a given potential. Proc. Nat. Acad. Sci. U.S.A., 47, 122-129 (1961) MR23 #B2833
27. [27] B. Simon: The bound state of weakly coupled Schrödinger operators on one and two dimensions. Ann. Physics, 97 (2), 279-288, (1976) Zbl0325.35029MR53 #8646
28. [28] Weidl, T.: On the Lieb-Thirring constants Lγ,1 for γ ≥ 1/2. Comm. Math. Phys., 178, 135-146 (1996) Zbl0858.34075MR97c:81039
29. [29] Weidl, T.: Remarks on virtual bound states for semi-bounded operators. Comm. Part. Diff. Equ., 24 (1&2), 25-60, (1999) Zbl0926.47009MR2000a:47031