Abstract
Inequalities of Lieb-Thirring type are established. Applications of these inequalities to estimates of the spectrum of unbounded operators are given.
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References
D. S. Barsegyan, “On the possibility of strengthening the Lieb-Thirring inequality,” Mat. Zametki 86(6), 803–818 (2009) [Math. Notes 86 (5–6), 753–766 (2009)].
B. S. Kashin, “On a class of inequalities for orthonormal systems,” Mat. Zametki 80(2), 204–208 (2006) [Math. Notes 80 (1–2), 199–203 (2006)].
E. H. Lieb and W. E. Thirring, “Inequalities for themoments of the eigenvalues of the Schrödinger Hamiltonian and their relation to Sobolev inequalities,” in Studies in Mathematical Physics. Essays in Honor of Valentine Bargmann (Princeton Univ. Press, Princeton, NJ, 1976), pp. 269–303.
A. A. Il’in, “Lieb-Thirring integral inequalities and their applications to attractors of Navier-Stokes equations,” Mat. Sb. 196(1), 33–66 (2005) [Russian Acad. Sci. Sb. Math. 196 (1), 29–61 (2005)].
S. V. Astashkin, “Lieb-Thirring inequality for L p norms,” Mat. Zametki 83(2), 163–169 (2008) [Math. Notes 83 (1–2), 145–151 (2008)].
A. M. Molchanov, “On conditions for the discreteness of the spectrum of self-adjoint differential operators of second order,” in Trudy Moskov. Mat. Obshch. (Izd. Moskov. Univ., Moscow, 1953), Vol. 2, pp. 169–199 [in Russian].
Mathematical Encyclopedia (Sovetskaya Entsiklopediya, Moscow, 1982), Vol. 3 [in Russian].
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Original Russian Text © D. S. Barsegyan, 2010, published in Matematicheskie Zametki, 2010, Vol. 88, No. 2, pp. 173–177.
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Barsegyan, D.S. Applications of inequalities of Lieb-Thirring type to spectral theory. Math Notes 88, 160–164 (2010). https://doi.org/10.1134/S0001434610070151
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DOI: https://doi.org/10.1134/S0001434610070151