
http://yadda.icm.edu.pl:80/baztech/element/bwmeta1.element.baztech-9b2a6859-130b-4c2b-9384-7f8e62587eb2

Czasopismo |
Opuscula Mathematica |
|||||||||||||
Tytuł artykułu |
Inversion of the Riemann-Liouville operator and its dual using wavelets |
|||||||||||||
Autorzy | Baccar, C. Hamadi, N. B. Herch, H. Meherzi, F. | |||||||||||||
Treść / Zawartość | ||||||||||||||
Warianty tytułu |
|
|||||||||||||
Języki publikacji | EN | |||||||||||||
Abstrakty |
|
|||||||||||||
Słowa kluczowe |
|
|||||||||||||
Wydawca |
AGH University of Science and Technology Press |
|||||||||||||
Czasopismo | Opuscula Mathematica | |||||||||||||
Rocznik | 2015 | |||||||||||||
Tom | Vol. 35, no. 6 | |||||||||||||
Strony | 867--887 | |||||||||||||
Opis fizyczny | Bibliogr. 30 poz. | |||||||||||||
Twórcy |
|
|||||||||||||
Bibliografia |
[1] M. Agranovsky, P. Kuchment, E.T. Quinto, Range descriptions for the spherical mean Radon transform, J. Funct. Anal. 248 (2007) 2, 344-386.
[2] L.E. Andersson, On the determination of a function from spherical averages, SIAM J. Math. Anal. 19 (1988) 1, 214-234. [3] L.E. Andersson, H. Helesten, An inverse method for the processing of synthetic aperture radar data, Inverse Problems 3 (1987) 1, 111-124. [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. [7] J. Cohen, N. Bleistein, Velocity inversion procedure for acoustic waves, Geophysics 44 (1979) 6, 1077-1087. [8] I. Daubechies, The wavelet transform,, time-frequency localization and signal analysis, IEEE Trans. Inform. Theory 36 (1990) 5, 961-1005. [9] A. Erdely, W. Magnus, F. Oberhettinger, F.G. Tricomi, Higher Transcendental Functions II, McGraw-Hill, New York, 1953. [10] J.A. Fawcett, Inversion of N-dimensional spherical averages, SIAM J. Appl. Math. 45 (1985) 2, 336-341. [11] E. Foufoula-Georgiou, P. Kumar, Wavelets in Geophysics, vol. 4 ol Wavelet Analysis and Its Applications, Academic Press, New York, 1994. [12] A. Grossman, J. Morlet, T. Paul, Transforms associated to square integrable group representations I. General results, J. Math. Phys. 26 (1985), 2473-2479. [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. [15] S. Helgason, The Radon Transform, Birkhauser, Boston, 1999. [16] M. Herberthson, A numerical implementation of an inverse formula for CARABAS Raw Data, National Defense Research Institute, Internal Report, D 30430-3.2, FOA, Linkóping, Sweden, 1986. [17] W. Joines, Y. Zhang, C. Li, R. Jirtle, The measured electrical properties of normal and malignant human tissue from 50 to 900 Mhz, Med. Phys. 21 (1994) 4, 547-550. [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. [20] N.N. Lebedev, Special Functions and Their Applications, Courier Dover Publications, New York, 1972. [21] D. Ludwig, The Radon transform, on euclidean space, Comm. Pure Appl. Math. 19 (1966) 1, 49-81. [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. [27] E.M. Stein, Interpolation of linear operators, Trans. Amer. Math. Soc. 83 (1956) 2, 482-492. [28] K. Trimeche, Weyl integral transform, and Paley-Wiener theorem associated with a singular differential operator on (0,+oo), J. Math. Pures Appl. 60 (1981), 51-98 [in French]. [29] K. Trimeche, Inversion of the Lions transmutation operators using generalized wavelets, Appl. Comput. Harmon. Anal. 4 (1997) 1, 97-112. [30] G.N. Watson, A Treatise on the Theory of Bessel Functions, Cambridge University Press, Cambridge, 1995. |
|||||||||||||
Kolekcja | BazTech | |||||||||||||
Identyfikator YADDA | bwmeta1.element.baztech-9b2a6859-130b-4c2b-9384-7f8e62587eb2 | |||||||||||||
Identyfikatory |
|