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

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Rocznik
Strony
867--887
Opis fizyczny
Bibliogr. 30 poz.
Twórcy
autor
  • Higher Institute of Informatics of El Manar 2 Department of Applied Mathematics Rue Abou Raihan El Bayrouni - 2080 Ariana, Tunisia
autor
  • Preparatory Institute for Engineering Studies El Manar Department of Mathematics 2092 El Manar 2 Tunis, Tunisia
autor
autor
Bibliografia
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  • [4] C. Baccar, N.B. Hamadi, L.T. Rachdi, Inversion formulas for the Riemann-Liouville transform and its dual associated with singular partial differential operators, Int. J. Math. Math. Sci. 2006 (2006) 86238, 1-26.
  • [5] C. Baccar, N.B. Hamadi, L.T. Rachdi, Best approximation for Weierstrass transform, connected with Riemann-Liouville operator, Commun. Math. Anal. 5 (2008) 1, 65-83.
  • [6] C. Baccar, L.T. Rachdi, Spaces of I)lv-type and a convolution product associated with the Riemann-Liouville operator, Bull. Math. Anal. Appl. 1 (2009) 3, 16-41.
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  • [9] A. Erdely, W. Magnus, F. Oberhettinger, F.G. Tricomi, Higher Transcendental Functions II, McGraw-Hill, New York, 1953.
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  • [13] A. Grossman, J. Morlet, T. Paul, Transforms associated to square integrable group representations II. Examples, Ann. Henri Poincare 45 (1986), 293-309.
  • [14] N.B. Hamadi, L.T. Rachdi, Weyl transforms associated with, the Riemann-Liouville operator, Int. J. Math. Sci. 2006 (2006), 94768, 1-19.
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  • [18] T.H. Koornwinder, The continuous wavelet transform, [in:] Wavelets: An Elementary Treatment of Theory and Applications, vol. 1 of Series in Approximations and Decompo­sitions, World Scientific, Singapore, 1993, 27-48.
  • [19] R.S. Laugesen, N. Weaver, G.L. Weiss, E.N. Wilson, A characterization of the higher-dimensional groups associated with continuous wavelets, J. Geom. Anal. 12 (2002) 1, 89-102.
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  • [22] Y. Meyer, Wavelets and Operators, vol. 1 of Cambridge Studies in Advanced Mathematics, Cambridge University Press, Cambridge, 1995.
  • [23] M.M. Nessibi, L.T. Rachdi, K. Trimeche, Ranges and inversion formulas for spherical mean operator and its dual, J. Math. Anal. Appl. 196 (1995) 3, 861-884.
  • [24] M.M. Nessibi, K. Trimeche, Inversion of the Radon transform on the Laguerre hypergroup by using generalized wavelets, J. Math. Anal. Appl. 208 (1997) 2, 337-363.
  • [25] S. Omri, L.T. Rachdi, Heisenberg-Pauli-Weyl uncertainty principle for the Riemann--Liouville operator, J. Inequal. Pure Appl. Math. 9 (2008) 3, Art. 88, 23 pp.
  • [26] D.C. Solmon, Asymptotic formulas for the dual Radon transform, Math. Z. 195 (1987) 3, 321-343.
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  • [30] G.N. Watson, A Treatise on the Theory of Bessel Functions, Cambridge University Press, Cambridge, 1995.
Typ dokumentu
Bibliografia
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