American Institute of Mathematical Sciences

2013, 2013(special): 247-257. doi: 10.3934/proc.2013.2013.247

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, United States 2 Department of Mathematics, University of Hull, Cottingham Road, Hull HU6 7RX, United Kingdom 3 1133 N Desert Deer Pass, Green Valley, Arizona 85614-5530, United States

Received  September 2012 Revised  April 2013 Published  November 2013

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.
Citation: Charles Fulton, David Pearson, Steven Pruess. Characterization of the spectral density function for a one-sided tridiagonal Jacobi matrix operator. Conference Publications, 2013, 2013 (special) : 247-257. doi: 10.3934/proc.2013.2013.247
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