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Applicable Analysis
An International Journal
Volume 89, 2010 - Issue 10
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Original Articles

Nonlinear Dunkl-wave equations

Pages 1645-1668 | Received 18 Mar 2009, Accepted 27 Apr 2010, Published online: 15 Sep 2010

References

  • Dunkl , CF . 1989 . Differential-difference operators associated to reflection group . Trans. Am. Math. Soc. , 311 : 167 – 183 .
  • Baker , TH and Forrester , PJ . 1998 . Non symmetric Jack polynomials and integral kernels . Duke Math. J. , 95 : 1 – 50 .
  • van Diejen , JF and Vinet , L . 2000 . Calogero-Sutherland-Moser Models, CRM Series in Mathematical Physics , New York : Springer-Verlag .
  • Hikami , K . 1996 . Dunkl operators formalism for quantum many-body problems associated with classical root systems . J. Phys. Soc. Japan , 65 : 394 – 401 .
  • Kakei , S . 1996 . Common algebraic structure for the Calogero-Sutherland models . J. Phys. A , 29 : 619 – 624 .
  • Lapointe , L and Vinet , L . 1996 . Exact operator solution of the Calogero-Sutherland model . Commun. Math. Phys. , 178 : 425 – 452 .
  • Ben Saïd , S and Ørsted , B . 2005 . The wave equation for Dunkl operators . Indag. Math. , 16 : 351 – 391 .
  • Dunkl , CF . 1992 . Hankel transforms associated to finite reflection groups . Contemp. Math. , 138 : 123 – 138 .
  • Mejjaoli , H . 2008 . Strichartz estimates for the Dunkl wave equation and applications . J. Math. Anal. Appl. , 346 ( 1 ) : 41 – 54 .
  • Mejjaoli , H . 2009 . Dispersion phenomena in Dunkl-Schrödinger equation and applications . Serdica Math. J. , 35 : 25 – 60 .
  • Mejjaoli , H . 2010 . Global well-posedness and scattering for a class of nonlinear Dunkl-Schrödinger equations . Nonlinear Anal.: Theory, Methods Appl. , 72 ( 1, 3–4 ) : 1121 – 1139 .
  • Rösler , M . 1998 . Hermite polynomials and the heat equation for Dunkl operators . Commun. Math. Phys. , 192 : 519 – 542 .
  • Ginibro , HJ and Velo , G . 1985 . The global Cauchy problem for nonlinear Klein-Gordon equation . Math. Z , 189 : 487 – 505 .
  • Ginibro , HJ , Soffer , A and Velo , G . 1992 . The global Cauchy problem for the critical nonlinear wave equations . J. Funct. Anal. , 110 : 96 – 130 .
  • Gérard , P . 1996 . Oscillations and concentration effects in semilinear dispersive wave equations . J. Funct. Anal. , 141 : 60 – 98 .
  • Dunkl , CF . 1991 . Integral kernels with reflection group invariant . Can. J. Math. , 43 : 1213 – 1227 .
  • De Jeu , MFE . 1993 . The Dunkl transform . Invent. Math. , 113 : 147 – 162 .
  • Rösler , M . 1999 . Positivity of Dunkl's intertwining operator . Duke. Math. J. , 98 : 445 – 463 .
  • Rösler , M . 2003 . A positive radial product formula for the Dunkl kernel . Trans. Am. Math. Soc. , 355 : 2413 – 2438 .
  • Thangavelu , S and Xu , Y . 2005 . Convolution operator and maximal functions for Dunkl transform . J. Anal. Math. , 97 : 25 – 56 .
  • Trimèche , K . 2001 . The Dunkl intertwining operator on spaces of functions and distributions and integral representation of its dual . Integ. Transf. Special Funct. , 12 ( 4 ) : 349 – 374 .
  • Trimèche , K . 2002 . Paley-Wiener theorems for Dunkl transform and Dunkl translation operators . Integ. Transf. Special Funct. , 13 : 17 – 38 .
  • Mejjaoli , H and Trimèche , K . 2004 . Hypoellipticity and hypoanalliticity associated with the Dunkl Laplacian . Integ. Transf. Special Funct. , 15 ( 6 ) : 523 – 548 .
  • Mejjaoli , H . 2008 . Dunkl hyperbolic equations . SIGMA , 4 084, (22 pages)
  • Mejjaoli , H . 2008 . Littlewood-Paley decomposition associated for the Dunkl operators and paraproduct operators . J. Inequal. Pure Appl. Math. , 9 ( 4 ) article 95, (25 pages)
  • Brezis , H . 1992 . Analyse Fonctionnelle. Théorie et Applications, 3 eme tirage , Paris, Milan, Barcelone, Bonn : Masson .

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