Inversion formulas in the Dunkl-type heat conduction on

References

• Asaduzzaman M Matsuura T Saitoh S Constructions of approximate solutions for linear differential equations by reproducing kernels and inverse problems 4th ISAAC Toronto Congress Proceedings (To appear)
   Google Scholar
• Baker , TH and Forrester , PJ . 1997 . The Calogero-Sutherland model and generalized classical polynomials . Communications in Mathematical Physics , 188 : 175 – 216 .
   Web of Science ®Google Scholar
• Byun D-W Saitoh S 1994 Best approximation in reproducing kernel Hilbert spaces Proceedings of the 2nd International Colloquium on Numerical Analysis, VSP-Holland 55 61
   Google Scholar
• Cherednik , L . 1991 . A unification of the Knizhnik-Zamolodchikov equation and Dunkl operators via affine Hecke Algebras . Inventiones Mathematicae , 106 : 411 – 432 .
   Web of Science ®Google Scholar
• Dunkl , CF . 1989 . Differential-difference operators associated with reflections groups . Transactions of the American Mathematical Society , 311 : 167 – 183 .
   Web of Science ®Google Scholar
• Dunkl , CF . 1991 . Integral kernels with reflection group invariance . Canadian Journal of Mathematics , 43 : 1213 – 1227 .
   Web of Science ®Google Scholar
• de Jeu , MFE . 1993 . The Dunkl transform . Inventiones Mathematicae , 113 : 147 – 162 .
   Web of Science ®Google Scholar
• Lapointe , L and Vinet , L . 1996 . Exact operator solution of the Calogero-Sutherland model . Communications in Mathematical Physics , 178 : 425 – 452 .
   Web of Science ®Google Scholar
• Matsuura T Saitoh S Trong DD 2004 Approximate and analytical inversion formulas in heat conduction on multidimensional spaces Journal of Inverse and Ill-posed Problems (In press)
   Google Scholar
• Opdam , EM . 1995 . Harmonic analysis for certain representations of graded Hecke Algebras . Acta Mathematica , 175 : 75 – 121 .
   Web of Science ®Google Scholar
• Rölsler , M . 1998 . Generalized Hermite polynomials and the heat equation for Dunkl operators . Communications in Mathematical Physics , 192 : 519 – 542 .
   Google Scholar
• Rösler , M . 1999 . Positivity of Dunkl's intertwining operator . Duke Mathematical Journal , 98 : 445 – 463 .
   Web of Science ®Google Scholar
• Rösler , M and Voit , M . 1998 . Markov processes related with Dunkl operator . Advances in Applied Mathematics , 21 : 575 – 643 .
   Web of Science ®Google Scholar
• Rösler , M and Voit , M . 1998 . Biorthogonal polynomials associated with reflection groups and a formula of Macdonald . Journal of Computational and Applied Mathematics , 99 : 337 – 351 .
   Google Scholar
• Saitoh , S . 1983 . The Weierestrass transform and an isometry in the heat equation . Applicable Analysis , 16 : 1 – 6 .
   Web of Science ®Google Scholar
• Saitoh , S . 2004 . Approximate real inversion formulas of the Gaussian convolution . Applicable Analysis , 83 : 727 – 733 .
   Google Scholar
• Sifi , M and Soltani , F . 2002 . Generalized Fock spaces and Weyl relations for the Dunkl kernel on the real line . Journal of Mathematical Analysis and Applications , 270 : 92 – 106 .
   Web of Science ®Google Scholar
• Soltani , F . 2004 . Lp -Fourier multipliers for the Dunkl operator on the real line . Journal of Functional Analysis , 209 : 16 – 35 .
   Web of Science ®Google Scholar
• Soltani , F . 2004 . Generalized Fock spaces and Weyl commutation relations for the Dunkl kernel . Pacific Journal of Mathematics , 214 : 379 – 397 .
   Web of Science ®Google Scholar
• Triméche , K . 2001 . The Dunkl intertwining operator on spaces of functions and distributions and integral representation of dual . Integral Transforms and Special Functions , 12 : 349 – 374 .
   Web of Science ®Google Scholar
• Triméche , K . 2002 . Paley-Wiener Theorems for the Dunkl transform and Dunkl translation operators . Integral Transforms and Special Functions , 13 : 17 – 38 .
   Web of Science ®Google Scholar