Geodesic
About a Conjecture on Difference Equations in Quasianalytic Carleman Classes
Publications de l'Institut Mathématique, _N_S_100 (2016) no. 114, p. 299 .

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We consider the difference equation $\sum_{j=1}^q a_j(x)\varphi(x+\alpha_j)=\chi(x)$ where $\alpha_1\dots\alpha_q$ ($q\geq 3$) are given real constants, $a_j$ ($j=1,\dots,q$) are given holomorphic functions on a strip $\mathbb{R}_{\delta }$ ($\delta>0$) such that $a_1$ and $a_q$ vanish nowhere on it, and $\chi$ is a function belonging to a quasianalytic Carleman class $C_M\{\mathbb{R}\}$. We prove, under a growth condition on the functions $a_j$, that the difference equation above is solvable in $C_M\{\mathbb{R}\}$.
DOI : 10.2298/PIM1614299Z
Classification : 30H05 30B10, 30D05
Keywords: difference equations, quasianalytic Carleman classes 
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     title = {About a {Conjecture} on {Difference} {Equations} in {Quasianalytic} {Carleman} {Classes}},
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Hicham Zoubeir. About a Conjecture on Difference Equations in Quasianalytic Carleman Classes. Publications de l'Institut Mathématique, _N_S_100 (2016) no. 114, p. 299 . doi : 10.2298/PIM1614299Z. http://geodesic.mathdoc.fr/articles/10.2298/PIM1614299Z/

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