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Asymptotic Formulas for Spectral and Weyl Functions of Sturm-Liouville Operators With Smooth Coefficients

  • Anne Boutet De Monvel
  • Vladimir Marchenko
Conference paper
Part of the Operator Theory: Advances and Applications book series (OT, volume 98)

Abstract

The exact asymptotic formulas are proved for the Weyl functions and spectral functions of Sturm-Liouville operators with smooth coefficients Let l be the differential operation where q is a real continuous potential. For τ = tan α we denote a selfadjoint extension in L 2 (ℝ) of the symmetric operator defined by l, whose domain contains the set of smooth functions with compact support in ℝ, satisfying the boundary condition Further on we shall deal only with the boundary conditions y′(0) = 0 or y(0) = 0 and corresponding operators

Keywords

Spectral Function Differentiable Function Asymptotic Formula Recurrence Formula Tauberian Theorem 
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References

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    V.A. Marchenko, Sturm-Liouville operators and applications, Birkhäuser Verlag, 1986.Google Scholar
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Copyright information

© Springer Basel AG 1997

Authors and Affiliations

  • Anne Boutet De Monvel
    • 1
  • Vladimir Marchenko
    • 2
  1. 1.Institut de Mathématiques de Jussieu, CNRS UMR 9994, Laboratoire de Physique Mathématique et Géométrie, case 7012Université Paris 7 Denis DiderotParis Cedex 05France
  2. 2.Mathematical DivisionInstitute for Low Temperature PhysicsKharkivUkraine

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