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.

Full Text

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},
  MRNUMBER = {MR2907357},
       URL = {http://mfat.imath.kiev.ua/article/?id=596},
}