A q-difference operator with discrete and simple spectrum

Authors

  • H. D. Voulov Department of Mathematics, University of Pittsburgh at Johnstown, Johnstown, PA, USA
  • M. J. Bohner Department of Mathematics and Statistics, Missouri University of Science and Technology, Rolla, MO, USA
  • M. B. Bekker Department of Mathematics and Statistics, University of Missouri-Kansas City, Kansas City, MO, USA 

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Keywords:

Abstract

We continue our study of a $q$-difference version of a second-order differential operator which depends on a real parameter. This version was introduced in our previous article. For values of the parameter for which the difference operator is self adjoint, we show that the spectrum of the operator is discrete and simple. When $q$ approaches $1$, the spectrum fills the whole positive or negative semiaxis.

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Published

2011-12-25

Issue

Vol. 17 No. 4 (2011)

Section

Articles

How to Cite

Voulov, H. D., et al. “A Q-Difference Operator With Discrete and Simple Spectrum”. Methods of Functional Analysis and Topology, vol. 17, no. 4, Dec. 2011, pp. 281-94, https://zen.imath.kiev.ua/index.php/mfat/article/view/493.