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

Pages: 247 - 257, Issue special, November 2013

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Charles Fulton - Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, FL, 32901-6975, United States (email)
David Pearson - Department of Mathematics, University of Hull, Cottingham Road, Hull HU6 7RX, United Kingdom (email)
Steven Pruess - 1133 N Desert Deer Pass, Green Valley, Arizona 85614-5530, United States (email)

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.

Keywords:  Periodic Jacobi matrix, discrete Schrödinger operator, Floquet solutions, Hill discriminant, absolutely continuous spectrum, stability intervals.
Mathematics Subject Classification:  Primary: 39A70, 39A23; Secondary: 47B36, 47B39, 47A75.

Received: September 2012;      Revised: April 2013;      Published: November 2013.