Article
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
Keywords:
differential-difference operator; generalized Fourier transform; Hardy and Cowling-Price theorems
differential-difference operator; generalized Fourier transform; Hardy and Cowling-Price theorems
Summary:
This paper is aimed to establish Hardy and Cowling-Price type theorems for the Fourier transform tied to a generalized Cherednik operator on the real line.
References:
[1] Ben Farah S., Mokni K.: Uncertainty principle and $L^p-L^q$ sufficient pairs on noncompact real symmetric spaces. C.R. Acad. Sci. Paris 336 (2003), 889–892. DOI 10.1016/S1631-073X(03)00220-6 | MR 1994589 | Zbl 1026.43009
[2] Ben Farah S., Mokni K., Trimèche K.: An $L^p-L^q$-version of Hardy's theorem for spherical Fourier transform on semi-simple Lie groups. Int. J. Math. Math. Sci. 33 (2004), 1757–1769. DOI 10.1155/S0161171204209140
[3] Cherednik I.: A unification of Knizhnik-Zamolodchikov equations and Dunkl operators via affine Hecke algebras. Invent. Math. 106 (1991), 411–432. DOI 10.1007/BF01243918 | MR 1128220
[4] Cowling M.G., Price J.F.: Generalisations of Heisenberg's inequality. Lecture Notes in Mathematics, 992, Springer, Berlin, 1983, pp. 443–449. DOI 10.1007/BFb0069174 | MR 0729369 | Zbl 0516.43002
[5] Eguchi M., Korzumi S., Kumahara K.: An $L^p$ version of the Hardy theorem for the motion group. J. Austral. Math. Soc. Ser. A 68 (2000), 55–67. DOI 10.1017/S1446788700001579 | MR 1727227
[6] Fitouhi A.: Heat polynomials for a singular differential operator on $(0,\infty)$. J. Constr. Approx. 5 (1989), 241–270. DOI 10.1007/BF01889609 | MR 0989675 | Zbl 0696.41027
[7] Gallardo L., Trimèche K.: Positivity of the Jacobi-Cherednik intertwining operator and its dual. Adv. Pure Appl. Math. 1 (2010), no. 2, 163–194. DOI 10.1515/apam.2010.011 | MR 2679886 | Zbl 1208.47027
[8] Hardy G.H.: A theorem concerning Fourier transform. J. London Math. Soc. 8 (1933), 227–231. DOI 10.1112/jlms/s1-8.3.227
[9] Heckman G.J., Schlichtkrull H.: Harmonic Analysis and Special Functions on Symmetric Spaces. Academic Press, San Diego, CA, 1994. MR 1313912 | Zbl 0836.43001
[10] Koornwinder T.H.: A new proof of a Paley-Wiener type theorem for the Jacobi transform. Ark. Mat. 13 (1975), 145–159. DOI 10.1007/BF02386203 | MR 0374832 | Zbl 0303.42022
[11] Mourou M.A.: Transmutation operators and Paley-Wiener theorem associated with a Cherednik type operator on the real line. Anal. Appl. (Singap.) 8 (2010), no. 4, 387–408. DOI 10.1142/S0219530510001692 | MR 2726071 | Zbl 1200.42003
[12] Opdam E.: Dunkl Operators for Real and Complex Reflection Groups. MSJ Memoirs, 8, Mathematical Society of Japan, Tokyo, 2000. MR 1805058 | Zbl 0984.33001
[13] Schapira B.: Contributions to the hypergeometric function theory of Heckman and Opdam: sharp estimates, Schwartz spaces, heat kernel. Geom. Funct. Anal. 18 (2008), 222–250. DOI 10.1007/s00039-008-0658-7 | MR 2399102
[14] Trimèche K.: Inversion of the Lions transmutation operators using generalized wavelets. Appl. Comput. Harmon. Anal. 4 (1997), 97–112. DOI 10.1006/acha.1996.0206 | MR 1429682 | Zbl 0872.34059
[15] Trimèche K.: Cowling-Price and Hardy theorems on Chébli-Trimèche hypergroups. Glob. J. Pure Appl. Math. 1 (2005), no. 3, 286–305. MR 2243232 | Zbl 1122.43005
[16] Trimèche K.: The trigonometric Dunkl intertwining operator and its dual associated with the Cherednik operators and the Heckman-Opdam theory. Adv. Pure Appl. Math. 1 (2010), no. 3, 293–323. DOI 10.1515/apam.2010.015 | MR 2719369 | Zbl 1204.33028
[17] Trimèche K.: Harmonic analysis associated with the Cherednik operators and the Heckman-Opdam theory. Adv. Pure Appl. Math. 2 (2011), no. 1, 23–46. DOI 10.1515/apam.2011.022 | MR 2769308 | Zbl 1207.33024
Search
Partner of
