References
- Lieb EH, Thirring W. Inequalities for the moments of the eigenvalues of the Schrödinger Hamiltonian and their relation to Sobolev inequalities. Essays in Honor of Valentine Bargmann: Princeton; 1976. p. 269–303. (Studies in Math. Phys.).
- Aizenman M, Lieb EH. On semi-classical bounds for eigenvalues of Schrödinger operators. Phys Lett. 1978;66A:427–429. doi: 10.1016/0375-9601(78)90385-7
- Laptev A, Weidl T. Sharp Lieb–Thirring inequalities in high dimensions. Acta Mathematica. 2000;184:87–111. doi: 10.1007/BF02392782
- Laptev A, Weidl T. Recent results on Lieb–Thirring inequalities. Journées “Équations aux Dérivées Partielles (La Chapelle sur Erdre, 2000), Exp. No. XX, Univ. Nantes, Nantes, 2000.
- Weidl T. On the Lieb–Thirring constants Lγ,1 for γ≥1/2. Comm Math Phys. 1996;178:135–146. doi: 10.1007/BF02104912
- Hundertmark D, Lieb EH, Thomas LE. A sharp bound for an eigenvalue moment of the one-dimensional Schrödinger operator. Adv Theor Math Phys. 1998;2:719–731. doi: 10.4310/ATMP.1998.v2.n4.a2
- Hundertmark D, Laptev A, Weidl T. New bounds on the Lieb–Thirring constants. Inv Math. 2000;140:693–704. doi: 10.1007/s002220000077
- Dolbeault J, Laptev A, Loss M. Lieb–Thirring inequalities with improved constants. JEMS. 2008;10:1121–1126. doi: 10.4171/JEMS/142
- Frank RL, Hundertmark D, Jex M, et al. The Lieb–Thirring inequality revisited. JEMS. to appear.
- Ekholm T, Frank RL. On Lieb–Thirring inequalities for Schrödinger operators with virtual level. Commun Math Phys. 2006;264(3):725–740. doi: 10.1007/s00220-006-1521-z
- Ekholm T, Frank RL. Lieb–Thirring inequalities on the half-line with critical exponent. J Eur Math Soc. 2008;10(3):739–755. doi: 10.4171/JEMS/128
- Frank RL. A simple proof of Hardy–Lieb–Thirring inequalities. Comm Math Phys. 2009;290(2):789–800. doi: 10.1007/s00220-009-0759-7
- Frank RL, Lieb EH, Seiringer R. Hardy–Lieb–Thirring inequalities for fractional Schrödinger operators. J Amer Math Soc. 2007;21:925–950. doi: 10.1090/S0894-0347-07-00582-6
- Benguria R, Loss M. A simple proof of a theorem by Laptev and Weidl. Math Res Lett. 2000;7(2–3):195–203. doi: 10.4310/MRL.2000.v7.n2.a5
- Exner P, Laptev A, Usman M. On some sharp spectral inequalities for Schrödinger operators on semiaxis. Commun Math Phys. 2014;326(2):531–541. doi: 10.1007/s00220-014-1885-4
- Schimmer L. Improved sharp spectral inequalities for Schrödinger operators on the semi-axis. 2019; arXiv:1912.13264.
- Abramowitz M, Stegun GA. Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables. National Bureau of Standards. 1972. (Applied Mathematical Series; 55).