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ArticleOriginal scientific text

Title

On the eigenvalue asymptotics of certain Schrödinger operators

Authors 1

Affiliations

  1. Institute of Mathematics, Polish Academy of Sciences, Wrocław Branch, Kopernika 18, 51-617 Wrocław, Poland

Abstract

Subelliptic estimates on nilpotent Lie groups and the Cwikel-Lieb-Rosenblum inequality are used to estimate the number of eigenvalues for Schrödinger operators with polynomial potentials.

Bibliography

  1. W. Cupała, On the essential spectrum and eigenvalue asymptotics of certain Schrödinger operators, Studia Math. 96 (1990), 195-202.
  2. Ch. L. Fefferman, The uncertainty principle, Bull. Amer. Math. Soc. 9 (1983), 129-206.
  3. G. B. Folland, Subelliptic estimates and function spaces on nilpotent Lie groups, Ark. Mat. 13 (1975), 161-207.
  4. K. Löwner, Über monotone Matrixfunktionen, Math. Z. 38 (1934), 177-216.
  5. B. Simon, Functional Integration and Quantum Physics, Academic Press, 1979.
Studia Mathematica
1993/105/1
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Pages:
101-104
Main language of publication
English
Received
1992-11-25
Accepted
1993-02-08
Published
1993
Exact and natural sciences