Geodesic
Nonlocal Operational Calculi for Dunkl Operators
Symmetry, integrability and geometry: methods and applications, Tome 5 (2009) Cet article a éte moissonné depuis la source Math-Net.Ru

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The one-dimensional Dunkl operator $D_k$ with a non-negative parameter $k$, is considered under an arbitrary nonlocal boundary value condition. The right inverse operator of $D_k$, satisfying this condition is studied. An operational calculus of Mikusiński type is developed. In the frames of this operational calculi an extension of the Heaviside algorithm for solution of nonlocal Cauchy boundary value problems for Dunkl functional-differential equations $P(D_k)u=f$ with a given polynomial $P$ is proposed. The solution of these equations in mean-periodic functions reduces to such problems. Necessary and sufficient condition for existence of unique solution in mean-periodic functions is found.
Keywords: Dunkl operator; right inverse operator; Dunkl–Appell polynomials; convolution multiplier; multiplier fraction; Dunkl equation; nonlocal Cauchy problem; Heaviside algorithm; mean-periodic function. 
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     author = {Ivan H. Dimovski and Valentin Z. Hristov},
     title = {Nonlocal {Operational} {Calculi} for {Dunkl} {Operators}},
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     url = {http://geodesic.mathdoc.fr/item/SIGMA_2009_5_a29/}
}
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Ivan H. Dimovski; Valentin Z. Hristov. Nonlocal Operational Calculi for Dunkl Operators. Symmetry, integrability and geometry: methods and applications, Tome 5 (2009). http://geodesic.mathdoc.fr/item/SIGMA_2009_5_a29/

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