Spectral Theory from the Second-Order q-Difference Operator
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...
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| Format: | Article |
| Language: | English |
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Wiley
2007-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2007/16595 |
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| _version_ | 1832564640324780032 |
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| author | Lazhar Dhaouadi |
| author_facet | Lazhar Dhaouadi |
| author_sort | Lazhar Dhaouadi |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-dab8d5c8e2624c36ac3e2bbe34bfd3c5 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2007-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-dab8d5c8e2624c36ac3e2bbe34bfd3c52025-02-03T01:10:34ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252007-01-01200710.1155/2007/1659516595Spectral Theory from the Second-Order q-Difference OperatorLazhar Dhaouadi0Institut Préparatoire aux Etudes d'Ingénieur de Bizerte, Université du 7 novembre Carthage, Route Menzel Abderrahmene Bizerte, Zarzouna 7021, TunisiaSpectral 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.http://dx.doi.org/10.1155/2007/16595 |
| spellingShingle | Lazhar Dhaouadi Spectral Theory from the Second-Order q-Difference Operator International Journal of Mathematics and Mathematical Sciences |
| title | Spectral Theory from the Second-Order q-Difference Operator |
| title_full | Spectral Theory from the Second-Order q-Difference Operator |
| title_fullStr | Spectral Theory from the Second-Order q-Difference Operator |
| title_full_unstemmed | Spectral Theory from the Second-Order q-Difference Operator |
| title_short | Spectral Theory from the Second-Order q-Difference Operator |
| title_sort | spectral theory from the second order q difference operator |
| url | http://dx.doi.org/10.1155/2007/16595 |
| work_keys_str_mv | AT lazhardhaouadi spectraltheoryfromthesecondorderqdifferenceoperator |