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

Charles Fulton; David Pearson; Steven Pruess

doi:10.3934/proc.2013.2013.247

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2013, Volume 2013: 247-257. Doi: 10.3934/proc.2013.2013.247 open access

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

1.
Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, FL, 32901-6975
2.
Department of Mathematics, University of Hull, Cottingham Road, Hull HU6 7RX
3.
1133 N Desert Deer Pass, Green Valley, Arizona 85614-5530

Received: August 31, 2012

Revised: March 31, 2013

Published: October 2013

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Abstract

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.

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Mathematics Subject Classification: Primary: 39A70, 39A23; Secondary: 47B36, 47B39, 47A75.

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References

[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. Pruess, Algorithms 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.