Absolute Continuity of Spectral Measure for Certain Unbounded Jacobi Matrices

  • Ryszard Szwarc
Part of the ISNM International Series of Numerical Mathematics book series (ISNM, volume 142)


Spectral properties of unbounded symmetric Jacobi matrices are studied. Under mild assumptions on the coefficients absolute continuity of spectral measure is proved. Only operator theoretic proofs are provided. Some open problems of Ifantis are solved.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Akhiezer, N.I., The Classical Moment Problem, Hafner Publ. Co., New York, 1965.zbMATHGoogle Scholar
  2. [2]
    T. Chihara, An Introduction to Orthogonal Polynomials, Mathematics and Its Applications, Vol. 13, Gordon and Breach, New York, London, Paris, 1978.Google Scholar
  3. [3]
    T. Chihara, Chain sequences and orthogonal polynomials, Trans. Amer. Math. Soc., 104 (1962), 1–16.MathSciNetzbMATHCrossRefGoogle Scholar
  4. [4]
    J. Dombrowski and P. Nevai, Orthogonal polynomials, measures and recurrence relations, SIAM J. Math. Anal., 17 (1986), 752–759.MathSciNetzbMATHGoogle Scholar
  5. [5]
    E.K. Ifantis, On the spectral measure of a class of orthogonal polynomials, J. Comp. Appl. Math., 133 (2001), 688–689.MathSciNetCrossRefGoogle Scholar
  6. [6]
    J. Janas and M. Moszynski, Alternative approaches to the absolute continuity of Jacobi matrices with monotonic weights,Int. Eq. Oper. Theory, (to appear).Google Scholar
  7. [7]
    S. Khan and D.B. Pearson, Subordinacy and spectral theory for inifinite matrices, Heiv. Phys. Acta 65 (1992), 505–527.Google Scholar
  8. [8]
    A. Maté and P. Nevai, Orthogonal polynomials and absolutely continuous measures, In C.K. Chui et al., editor, Approximation Theory IV, Vol. 103, Academic Press, New York, (1983), 611–617.Google Scholar
  9. [9]
    B. Simon, The classical moment problem as a self-adjoint finite difference operator, Advances Math. 137 (1998), 82–203.zbMATHCrossRefGoogle Scholar

Copyright information

© Birkhäuser Verlag Basel 2002

Authors and Affiliations

  • Ryszard Szwarc
    • 1
  1. 1.Institute of MathematicsWrocław UniversityWrocławPoland

Personalised recommendations