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International Journal of Mathematics and Mathematical Sciences
Volume 2007 (2007), Article ID 16595, 14 pages
Research Article

Spectral Theory from the Second-Order q-Difference Operator

Institut Préparatoire aux Etudes d'Ingénieur de Bizerte, Université du 7 novembre Carthage, Route Menzel Abderrahmene Bizerte, Zarzouna 7021, Tunisia

Received 24 October 2006; Revised 28 January 2007; Accepted 28 February 2007

Academic Editor: Petru Jebelean

Copyright © 2007 Lazhar Dhaouadi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Spectral theory from the second-order q-difference operator Δq is developed. We give an integral representation of its inverse, and the resolvent operator is obtained. As application, we give an analogue of the Poincare inequality. We introduce the Zeta function for the operator Δq and we formulate some of its properties. In the end, we obtain the spectral measure.