Best approximation of the Dunkl Multiplier Operators Tk,â„“,m
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Abstract
We study some class of Dunkl multiplier operators Tk,â„“,m; and we give for them an application of the theory of reproducing kernels to the Tikhonov regularization,which gives the best approximation of the operators Tk,â„“,m on a Hilbert spaces Hskâ„“.
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References
- C.F. Dunkl, Integral kernels with reflection group invariance, Canad. J. Math. 43 (1991) 1213- 1227.
- C.F. Dunkl, Hankel transforms associated to finite reflection groups, Contemp. Math. 138 (1992) 123-138.
- M.F.E.de Jeu, The Dunkl transform, Invent. Math. 113 (1993) 147-162.
- G.S. Kimeldorf and G. Wahba, Some results on Tchebycheffian spline functions, J. Math. Anal. Appl. 33 (1971) 82-95.
- T. Matsuura, S. Saitoh and D.D. Trong, Inversion formulas in heat conduction multidimensional spaces, J. Inv. Ill-posed Problems 13 (2005) 479-493.
- M. R ¨osler and M. Voit, Markov processes related with Dunkl operators, Adv. Appl. Math. 21 (1998) 575-643.
- E.M. Opdam, Dunkl operators, Bessel functions and the discriminant of a finite Coxeter group, Compositio Math. 85(3) (1993) 333-373.
- S. Saitoh, Hilbert spaces induced by Hilbert space valued functions, Proc. Amer. Math. Soc. 89 (1983) 74-78.
- S. Saitoh, The Weierstrass transform and an isometry in the heat equation, Appl. Anal. 16 (1983) 1-6.
- S. Saitoh, Approximate real inversion formulas of the Gaussian convolution, Appl. Anal. 83 (2004) 727-733.
- S. Saitoh, Best approximation, Tikhonov regularization and reproducing kernels, Kodai Math. J. 28 (2005) 359-367.
- F. Soltani, Inversion formulas in the Dunkl-type heat conduction on Rd, Appl. Anal. 84 (2005) 541-553.
- F. Soltani, Best approximation formulas for the Dunkl L2 -multiplier operators on Rd, Rocky Mountain J. Math. 42 (2012) 305-328.
- F. Soltani, Multiplier operators and extremal functions related to the dual Dunkl-Sonine operator, Acta Math. Sci. 33B(2) (2013) 430-442.
- F. Soltani, Operators and Tikhonov regularization on the Fock space, Int. Trans. Spec. Funct. 25(4) (2014) 283-294.
- F. Soltani, Uncertainty principles and extremal functions for the Dunkl L2 -multiplier operators, J. Oper. 2014 (2014), Article ID 659069.
- F. Soltani and A. Nemri, Analytical and numerical applications for the Fourier multiplier operators on Rn × (0, ∞), Appl. Anal. 2014, DOI:10.1080/00036811.2014.937432.
- M. Yamada, T. Matsuura and S. Saitoh, Representations of inverse functions by the integral transform with the sign kernel, Frac. Calc. Appl. Anal. 2 (2007) 161-168.