International Journal of Mathematics and Mathematical Sciences
Volume 2007 (2007), Article ID 16595, 14 pages
doi:10.1155/2007/16595

Spectral Theory from the Second-Order q-Difference Operator

Lazhar Dhaouadi

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

Abstract

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.