References
- L.C.Andrews, Special functions of Mathematics for engineers, second edition, Oxford University Press-Oxford-Tokyo-Melbourn, 1998.
- W.R.Bloom and H.Heyer, Harmonic analysis of probability measures on hypergroups, Walter de Grayter, Berlin, New-York 1995.
- I.Cherednik, Inverse Harish-Chandra transform and difference operators, Internat. Math. Res. Notices 15 (1997), 733-750.
- L.Gallardo and K.Trimeche, Positivity of the Jacobi-Cherednik intertwining operator and its dual, Adv. Pure Appl. Math. 1 (2012), 163-194.
- P.Goupilland, A.Grossmann and J.Morlet, Cycle octave and related transforms in seismic signal analysis, Geoexploration 23 (1984-1985), 85-102.
- A.Graussmann and J.Morlet, Decomposition of Hardy functions into square integrable wavelets of constant shape, Soc. Int. Am. Math. (SIAM), J. Math. Analys. 15 (1984), 723-736.
-
A.Hassini and K.Trimeche, Wavelets and generalized windowed transforms associated with the Dunkl-Bessel-Laplace operator on
${\mathbb{R}}^d{\time}{\mathbb{R}}_+$ , Mediterr. J. Math. 12 (2015), 1323-1344. https://doi.org/10.1007/s00009-015-0540-4 - G.J.Heckman and E.M.Opdam, Root systems and hypergeometric functions, I. Compositio Math. 64 (1987), 329-352.
- A.Jouini and K.Trimeche, Two versions of wavelets and applications, Narosa Publishing House, Pvt.Ltd, 2006.
- T.H.Koornwinder, A new proof of the Paley-Wiener type theorem for the Jacobi transform, Arkiv For Math. 13 (1) (1975), 145-159. https://doi.org/10.1007/BF02386203
- T.H.Koornwinder, The continuous wavelet transform. Series in Approximations and Decompositions. Vol. 1. Wavelets: An elementary treatment of theory and applications. Edited by T.H.Koornwinder, World Scientific, (1993), p. 27-48.
- E.M.Opdam, Harmonic analysis for certain representations of graded Hecke algebras, Acta Math. 175 (1995), 75-121. https://doi.org/10.1007/BF02392487
- B.Schapira, Contribution to the hypergeometric function theory of Heckman and Opdam; sharp estimates, Schwartz spaces, heat kernel, Geom. Funct. Anal. 18 (2008), 222-250. https://doi.org/10.1007/s00039-008-0658-7
- K.Trimeche, Generalized Wavelets and Hypergroups, Gordon and Breach Science Publishers, 1997.
- K.Trimeche, Paley-Wiener theorems for the Dunkl transform and Dunkl translation operators, Integ. Transf. and Spec. Funct. 13 (2002), 17-38. https://doi.org/10.1080/10652460212888
- K.Trimeche, The trigonometric Dunkl intertwining operator and its dual associated with the Cherednik operator and the Heckman Opdam theory, Adv. Pure Appl. Math. 1 (2010), 293-323.
- K.Trimeche, Harmonic analysis associated with the Cherednik operators and the Heckman-Opdam theory, Adv. Pure Appl. Math. 2 (2011), 23-46.
-
K.Trimeche, The positivity of the hypergeometric translation operators associated to the Cherednik operators and the Heckman-Opdam theory attached to the root systems of type
$B_2$ and$C_2$ , Korean J. Math. 22 (4) (2014), 711-728. https://doi.org/10.11568/kjm.2014.22.4.711 -
K.Trimeche, Positivity of the transmutation operators and absolute continuity of their representing measures for a root system on
${\mathbb{R}}^d$ , Int. J. App. Math. 28 (4) (2015), 427-453. -
K.Trimeche, The harmonic analysis associated to the Heckman-Opdam theory and its application to a root system of type
$BC_d$ ., Preprint. Faculty of Sciences of Tunis. 2015.
Cited by
- The hypergeometric Wigner and Weyl transforms attached to the Cherednik operators in the W-invariant case vol.28, pp.9, 2017, https://doi.org/10.1080/10652469.2017.1343315
- The Donoho–Stark, Benedicks and Heisenberg type uncertainty principles, and the localization operators for the Heckman–Opdam continuous wavelet transform on $${\mathbb {R}}^{d}$$ R d vol.8, pp.3, 2017, https://doi.org/10.1007/s11868-017-0194-z
- Boundedness and compactness of Heckman–Opdam two-wavelet multipliers vol.8, pp.4, 2017, https://doi.org/10.1007/s11868-017-0221-0
- The Wigner and Weyl transforms attached to the Heckman-Opdam-Jacobi theory on $${\mathbb {R}}^{d+1}$$ vol.12, pp.2, 2021, https://doi.org/10.1007/s11868-021-00404-z
- Time-frequency analysis associated with the generalized Wigner transform vol.32, pp.9, 2016, https://doi.org/10.1080/10652469.2020.1833329