Dunkl heat semigroup and applications

References

• Dunkl , CF . 1989 . Differential-difference operators associated to reflection group . Trans. Am. Math. Soc. , 311 : 167 – 183 .
   Web of Science ®Google Scholar
• Baker , TH and Forrester , PJ . 1998 . Non symmetric Jack polynomials and integral kernels . Duke Math. J. , 95 : 1 – 50 .
   Web of Science ®Google Scholar
• van Diejen , JF and Vinet , L . 2000 . Calogero–Sutherland-Moser Models, CRM Series in Mathematical Physics , Vol. 4 , New York : Springer-Verlag .
   Google Scholar
• Hikami , K . 1996 . Dunkl operators formalism for quantum many-body problems associated with classical root systems . J. Phys. Soc. Japan , 65 : 394 – 401 .
   Google Scholar
• Dunkl , CF . 1992 . Hankel transforms associated to finite reflection groups . Contemp. Math. , 138 : 123 – 138 .
   Google Scholar
• de Jeu , MFE . 1993 . The Dunkl transform . Invent. Math. , 113 : 147 – 162 .
   Web of Science ®Google Scholar
• Mejjaoli , H . 2008 . Strichartz estimates for the Dunkl wave equation and applications . J. Math. Anal. Appl. , 346 ( 1 ) : 41 – 54 .
   Web of Science ®Google Scholar
• Mejjaoli , H . 2009 . Dispersion phenomena in Dunkl-Schrödinger equation and applications . Serdica Math. J. , 35 : 25 – 60 .
   Google Scholar
• Mejjaoli , H . 2010 . Global well-posedness and scattering for a class of nonlinear Dunkl-Schrödinger equations . Nonlinear Anal.: Theory, Methods Appl. , 72 ( 3–4, 1 ) : 1121 – 1139 .
   Web of Science ®Google Scholar
• Mejjaoli , H . 2010 . Nonlinear Dunkl-wave equations . App. Anal. , 72 ( 3–4, 1 ) : 1121 – 1139 .
   Google Scholar
• Rösler , M . 1998 . Hermite polynomials and the heat equation for Dunkl operators . Commun. Math. Phys. , 192 : 519 – 542 .
   Web of Science ®Google Scholar
• Etingof , P . 2010 . A uniform proof of the Macdonald-Mehta-Opdam identity for finite Coxeter groups . Math. Res. Lett. , 17 : 277 – 284 .
   Web of Science ®Google Scholar
• Trimèche , K . 2002 . Paley-Wiener theorems for Dunkl transform and Dunkl translation operators . Intg. Transf. Spec. Funct. , 13 : 17 – 38 .
   Web of Science ®Google Scholar
• Thangavelu , S and Xu , Y . 2005 . Convolution operator and maximal functions for Dunkl transform . J. d'Analyse Mathematique , 97 : 25 – 56 .
   Web of Science ®Google Scholar
• Kawazoe , T and Mejjaoli , H . Generalized Besov spaces and their applications, Tokyo J. (to appear)
   Google Scholar
• Mejjaoli , H . Generalized nonhomogeneous Besov spaces and their applications, Serdica Math. J. (to appear)
   Google Scholar
• Mejjaoli , H and Trimèche , K . 2004 . Hypoellipticity and hypoanaliticity of the Dunkl Laplacian operator . Integ. Transf. Spec. Funct. , 15 ( 6 ) : 523 – 548 .
   Web of Science ®Google Scholar
• Mejjaoli , H . 2008 . Littlewood–Paley decomposition associated with the Dunkl operators, and paraproduct operators . J. Inequal. Pure Appl. Math. , 9 : 1 – 25 .
   Google Scholar
• Miao , C and Zhang , B . 2004 . The Cauchy problem for semilinear parabolic equations in Besov spaces . Houston J. Math. , 30 ( 3 ) : 829 – 878 .
   Web of Science ®Google Scholar
• Stein , EM and Weiss , G . 1971 . Introduction to Fourier Analysis on Euclidean Spaces , Princeton : Princeton University Press .
   Google Scholar
• Ginibro , HJ and Velo , G . 1979 . On a class of nonlinear Schrödinger equations . J. Funct. Anal. , 32 : 1 – 72 .
   Web of Science ®Google Scholar
• Keel , H and Tao , T . 1998 . Endpoint Strichartz estimates . Am. J. Math. , 120 : 955 – 980 .
   Web of Science ®Google Scholar
• Strichartz , RS . 1977 . Restriction of Fourier transform to quadratic surfaces and decay of solutions of wave equations . Duke Math. J. , 44 : 705 – 774 .
   Web of Science ®Google Scholar
• Tao , T . Global regularity of wave maps IV. Absence of stationary or self-similar solutions in the energy class. Available at http://www.lanl.arxiv.org/abs/08063592
   Google Scholar
• Tao , T . 2001 . Multilinear weighted convolution of L 2–functions, and applications to nonlinear dispersive equations . Am. J. Math. , 123 : 839 – 908 .
   Web of Science ®Google Scholar
• Gallardo , L and Trimèche , K . 2004 . An L p version of Hardy's theorem for the Dunkl transform . J. Aust. Math. Soc. , 77 : 371 – 385 .
   Web of Science ®Google Scholar