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Mathematical Notes

, Volume 82, Issue 3–4, pp 451–460 | Cite as

On inequalities of Lieb-Thirring type

  • D. S. BarsegyanEmail author
Mathematical Notes
  • 66 Downloads

Abstract

Applying the method proposed by Kashin for proving inequalities of Lieb-Thirring type for orthonormal systems, we prove a similar inequality in the multidimensional case.

Key words

Lieb-Thirring inequalities orthogonal series orthonormal system of functions normalized Lebesgue measure Rademacher system 

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References

  1. 1.
    E. Lieb and W. Thirring, “Inequalities for the moments of the eigenvalues of the Schrödinger Hamiltonian and their relation to Sobolev inequalities,” in Stud. Math. Phys., Essays in Honor of Valentine Bargmann (Princeton Univ. Press, Princeton, 1976), pp. 269–303.Google Scholar
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    A. A. Il’in, “Integral Lieb-Thirring inequalities and Their Applications to the Attractors of the Navier-Stokes Equations,” Mat. Sb. 196(1), 33–66 (2005) [Russian Acad. Sci. Sb. Math. 196 (1), 29–61 (2005)].MathSciNetGoogle Scholar
  3. 3.
    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)].MathSciNetGoogle Scholar
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    B. S. Kashin and A. A. Saakyan, Orthogonal Series (AFTs, Moscow, 1999) [in Russian].Google Scholar
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    S. M. Nikol’skii, Approximation of Functions of Several Variables and Embedding Theorems (Nauka, Moscow, 1977) [in Russian].Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2007

Authors and Affiliations

  1. 1.Yerevan State UniversityRussia

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