Spectral Theory from the Second-Order <mml:math id="E1" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>q</mml:mi></mml:math>-Difference Operator

Dhaouadi, Lazhar

doi:https://doi.org/10.1155/2007/16595

International Journal of Mathematics and Mathematical Sciences

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Research Article | Open Access

Volume 2007 | Article ID 016595 | https://doi.org/10.1155/2007/16595

Spectral Theory from the Second-Order q-Difference Operator

Lazhar Dhaouadi¹

Academic Editor: Petru Jebelean

Received24 Oct 2006

Revised28 Jan 2007

Accepted28 Feb 2007

Published21 Jun 2007

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.

References

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Copyright

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.

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