\`x^2+y_1+z_12^34\`
Advanced Search
Article Contents
Article Contents

Characterization of the spectral density function for a one-sided tridiagonal Jacobi matrix operator

Abstract Related Papers Cited by
  • In this paper we give a first order system of difference equations which provides a useful companion system in the study of Jacobi matrix operators and make use of it to obtain a characterization of the spectral density function for a simple case involving absolutely continuous spectrum on the stability intervals.
    Mathematics Subject Classification: Primary: 39A70, 39A23; Secondary: 47B36, 47B39, 47A75.

    Citation:

    \begin{equation} \\ \end{equation}
  • [1]

    M. Appell, Sur la transformation des équations différentielles linéaires, Comptes rendus hebdomadaires des seánces de l'Académie des sciences 91 (4) (1880), 211-214.

    [2]

    F.V. Atkinson, "Discrete and Continuous Boundary Problems," Academic Press, N.Y., 1964.

    [3]

    M.S.P. Eastham, "The Spectral Theory of periodic differential equations," Scottish Academic Press, London, 1973.

    [4]

    C.T. Fulton, D.B. Pearson, and S. Pruess, New characterizations of spectral density functions for singular Sturm-Liouville problems, J. Comput. Appl. Math (2008) 212 (2), pp. 194-213.

    [5]

    C.T. Fulton, D.B. Pearson, and S. Pruess, Efficient calculation of spectral density functions for specific classes of singular Sturm-Liouville problems, J. Comput. Appl. Math (2008) 212 (2), pp. 150-178.

    [6]

    C.T. Fulton, D.B. Pearson, and S. PruessAlgorithms for Estimating Spectral Density Functions for Periodic Potentials, preprint, arXiv:1303.5878.

    [7]

    C.T. Fulton, D.B. Pearson, and S. Pruess, Titchmarsh-Weyl theory for tridiagonal Jacobi matrices and computation of their spectral functions, in "Advances in nonlinear analysis: theory, methods and applications," (ed. S. Sivasundaram), Math Probl. Eng. Aerosp. Sci., 3, Camb. Sci. Publ.,(2009), 165-172.

    [8]

    B. Simon, "Szegö's Theorem and Its Descendants," Princeton University Press, Princeton, 2011.

    [9]

    G. Stolz and R. Weikard, "Notes of Seminar on Jacobi Matrices," Dept of Mathematics, University of Alabama, Birmingham, Jan. 2004.

    [10]

    G. Teschl, Jacobi Operators and Completely, Integrable Nonlinear Lattices, Mathematical Surveys and Monographs, Vol 72, Amer. Math. Soc., 2000.

  • 加载中
Open Access Under a Creative Commons license
SHARE

Article Metrics

HTML views() PDF downloads(80) Cited by(0)

Access History

Other Articles By Authors

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return