Inversion formulas for Riemann-Liouville transform and its dual associated with singular partial differential operators

Inversion formulas for Riemann-Liouville transform and its dual associated with singular partial differential operators

We define Riemann-Liouville transform ℛα and its dual tℛα associated with two singular partial differential operators. We establish some results of harmonic analysis for the Fourier transform connected with ℛα. Next, we prove inversion formulas for the operators ℛα, tℛα and a Plancherel theorem for...

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Main Authors: C. Baccar, N. B. Hamadi, L. T. Rachdi
Format: Article
Language:English
Published: Hindawi Limited 2006-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/IJMMS/2006/86238
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spelling doaj-09305aa0171744478351ada5f18506a02020-11-24T23:49:23ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252006-01-01200610.1155/IJMMS/2006/8623886238Inversion formulas for Riemann-Liouville transform and its dual associated with singular partial differential operatorsC. Baccar0N. B. Hamadi1L. T. Rachdi2Department of Mathematics, Faculty of Sciences of Tunis, University Tunis El Manar, 2092 Tunis, TunisiaDepartment of Mathematics, Faculty of Sciences of Tunis, University Tunis El Manar, 2092 Tunis, TunisiaDepartment of Mathematics, Faculty of Sciences of Tunis, University Tunis El Manar, 2092 Tunis, TunisiaWe define Riemann-Liouville transform ℛα and its dual tℛα associated with two singular partial differential operators. We establish some results of harmonic analysis for the Fourier transform connected with ℛα. Next, we prove inversion formulas for the operators ℛα, tℛα and a Plancherel theorem for tℛα.http://dx.doi.org/10.1155/IJMMS/2006/86238
collection DOAJ
language English
format Article
sources DOAJ
author C. Baccar
N. B. Hamadi
L. T. Rachdi
spellingShingle C. Baccar
N. B. Hamadi
L. T. Rachdi
Inversion formulas for Riemann-Liouville transform and its dual associated with singular partial differential operators
International Journal of Mathematics and Mathematical Sciences
author_facet C. Baccar
N. B. Hamadi
L. T. Rachdi
author_sort C. Baccar
title Inversion formulas for Riemann-Liouville transform and its dual associated with singular partial differential operators
title_short Inversion formulas for Riemann-Liouville transform and its dual associated with singular partial differential operators
title_full Inversion formulas for Riemann-Liouville transform and its dual associated with singular partial differential operators
title_fullStr Inversion formulas for Riemann-Liouville transform and its dual associated with singular partial differential operators
title_full_unstemmed Inversion formulas for Riemann-Liouville transform and its dual associated with singular partial differential operators
title_sort inversion formulas for riemann-liouville transform and its dual associated with singular partial differential operators
publisher Hindawi Limited
series International Journal of Mathematics and Mathematical Sciences
issn 0161-1712
1687-0425
publishDate 2006-01-01
description We define Riemann-Liouville transform ℛα and its dual tℛα associated with two singular partial differential operators. We establish some results of harmonic analysis for the Fourier transform connected with ℛα. Next, we prove inversion formulas for the operators ℛα, tℛα and a Plancherel theorem for tℛα.
url http://dx.doi.org/10.1155/IJMMS/2006/86238
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AT nbhamadi inversionformulasforriemannliouvilletransformanditsdualassociatedwithsingularpartialdifferentialoperators
AT ltrachdi inversionformulasforriemannliouvilletransformanditsdualassociatedwithsingularpartialdifferentialoperators
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