Opuscula Mathematica
Opuscula Math. 35, no. 6 (2015), 867-887

Inversion of the Riemann-Liouville operator and its dual using wavelets

C. Baccar
N. B. Hamadi
H. Herch
F. Meherzi
Abstract. We define and study the generalized continuous wavelet transform associated with the Riemann-Liouville operator that we use to express the new inversion formulas of the Riemann-Liouville operator and its dual.
Keywords: inverse problem, Riemann-Liouville operator, Fourier transform, wavelets.
Mathematics Subject Classification: 35R30, 42B10, 42C40.
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About the authors ▼
C. Baccar
Higher Institute of Informatics of El Manar 2, Department of Applied Mathematics, Rue Abou Raïhan El Bayrouni - 2080 Ariana, Tunisia
N. B. Hamadi
Department of Mathematics, Preparatory Institute for Engineering Studies El Manar, 2092 El Manar 2 Tunis, Tunisia
H. Herch
F. Meherzi
About the article ▼
Communicated by Semyon B. Yakubovich.
Received: 2014-11-10.
Revised: 2014-12-29.
Accepted: 2015-01-05.
Published online: 2015-06-06.
Cite this article as ▼
C. Baccar, N. B. Hamadi, H. Herch, F. Meherzi, Inversion of the Riemann-Liouville operator and its dual using wavelets, Opuscula Math. 35, no. 6 (2015), 867-887, http://dx.doi.org/10.7494/OpMath.2015.35.6.867.
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