Geodesic
Integro-differential-difference equations associated with the Dunkl operator and entire functions
Commentationes Mathematicae Universitatis Carolinae, Tome 45 (2004) no. 4, pp. 699-725.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

In this work we consider the Dunkl operator on the complex plane, defined by $$ \Cal D_k f(z)=\frac{d}{dz}f(z)+k\frac{f(z)-f(-z)}{z}, k\geq 0. $$ We define a convolution product associated with $\Cal D_k$ denoted $\ast_k$ and we study the integro-differential-difference equations of the type $\mu \ast_k f=\sum_{n=0}^{\infty}a_{n,k}\Cal D^n_k f$, where $(a_{n,k})$ is a sequence of complex numbers and $\mu $ is a measure over the real line. We show that many of these equations provide representations for particular classes of entire functions of exponential type.
Classification : 30D05, 30D15, 33E30, 34K99, 34M05, 44A35, 45J05
Keywords: Dunkl operator; Fourier-Dunkl transform; entire function of exponential type; integro-differential-difference equation 
@article{CMUC_2004__45_4_a10,
     author = {Salem, N\'ejib Ben and Kallel, Samir},
     title = {Integro-differential-difference equations associated with the {Dunkl} operator and entire functions},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {699--725},
     publisher = {mathdoc},
     volume = {45},
     number = {4},
     year = {2004},
     mrnumber = {2103085},
     zbl = {1098.30019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_2004__45_4_a10/}
}
TY  - JOUR
AU  - Salem, Néjib Ben
AU  - Kallel, Samir
TI  - Integro-differential-difference equations associated with the Dunkl operator and entire functions
JO  - Commentationes Mathematicae Universitatis Carolinae
PY  - 2004
SP  - 699
EP  - 725
VL  - 45
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMUC_2004__45_4_a10/
LA  - en
ID  - CMUC_2004__45_4_a10
ER  - 
%0 Journal Article
%A Salem, Néjib Ben
%A Kallel, Samir
%T Integro-differential-difference equations associated with the Dunkl operator and entire functions
%J Commentationes Mathematicae Universitatis Carolinae
%D 2004
%P 699-725
%V 45
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMUC_2004__45_4_a10/
%G en
%F CMUC_2004__45_4_a10
Salem, Néjib Ben; Kallel, Samir. Integro-differential-difference equations associated with the Dunkl operator and entire functions. Commentationes Mathematicae Universitatis Carolinae, Tome 45 (2004) no. 4, pp. 699-725. http://geodesic.mathdoc.fr/item/CMUC_2004__45_4_a10/