Open Access

# A q-difference operator with discrete and simple spectrum

### 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.

### Article Information

 Title A q-difference operator with discrete and simple spectrum Source Methods Funct. Anal. Topology, Vol. 17 (2011), no. 4, 281-294 MathSciNet MR2907357 Copyright The Author(s) 2011 (CC BY-SA)

### Authors Information

Miron B. Bekker
Department of Mathematics, University of Pittsburgh at Johnstown, Johnstown, PA, USA

Martin J. Bohner
Department of Mathematics and Statistics, Missouri University of Science and Technology, Rolla, MO, USA

Hristo Voulov
Department of Mathematics and Statistics, University of Missouri-Kansas City, Kansas City, MO, USA

### Citation Example

Miron B. Bekker, Martin J. Bohner, and Hristo Voulov, A q-difference operator with discrete and simple spectrum, Methods Funct. Anal. Topology 17 (2011), no. 4, 281-294.

### BibTex

@article {MFAT596,
AUTHOR = {Bekker, Miron B. and Bohner, Martin J. and Voulov, Hristo},
TITLE = {A q-difference operator with discrete and simple spectrum},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {17},
YEAR = {2011},
NUMBER = {4},
PAGES = {281-294},
ISSN = {1029-3531},
URL = {http://mfat.imath.kiev.ua/article/?id=596},
}