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

Article Contents

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: September 2012

Revised: April 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

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