Advertisement

New Proof of Trace Formulas in Case of Classical Sturm-Liouville Problem

  • B. M. Levitan
Conference paper
Part of the Operator Theory: Advances and Applications book series (OT, volume 98)

Abstract

A generalized trace formula for Sturm-Liouville operators is proved using the method of the wave equation.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    I. M. Gelfand and B. M. Levitan. On a simple identity for the eigenvalues of a differential operator of second order. Dokl. Akad. Nauk USSR 88, (1953), 593–596.MathSciNetGoogle Scholar
  2. [2]
    B. M. Levitan. On the asymptotic behavior of the spectral function of a self-adjoint differential equation of second order. Izv. Akad. Nauk USSR, Serie Math. 16 (1952), 325–352. English translation: Amer. Math. Soc. Transl. (2) 101 (1973), 192-221.MathSciNetzbMATHGoogle Scholar
  3. [3]
    B. M. Levitan. On the asymptotic behavior of the spectral function of a self-adjoint differential operator of second order. Izv. Akad. Nauk USSR, Serie Math. 17 (1953), 331–364. English translation:Amer.Math. Soc. Transl. 102 (1973), 191-229.MathSciNetzbMATHGoogle Scholar
  4. [4]
    H. Hochstadt. On the determination of Hill’s equation from its spectrum. Arch. Rat. Mech. Anal. 19 (1965), 353–362.MathSciNetzbMATHCrossRefGoogle Scholar
  5. [5]
    B. M. Levitan and I. S. Sargsjan Introduction to Spectral Theory. Transl. of Math. Monographs, Amer. Math. Soc. Providence, (1975)Google Scholar
  6. [6]
    G. N. Watson. A Treatise on the Theory of Bessel functions.Google Scholar
  7. [7]
    H. P. McKean and P. Van Moerbeke. The spectrum of HilVs equation. Invent. Math. 30 (1975), 217–274.MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer Basel AG 1997

Authors and Affiliations

  • B. M. Levitan
    • 1
  1. 1.School of MathematicsUniversity of MinneapolisMinneapolisUSA

Personalised recommendations