Publications de l’Institut Mathématique, Nouvelle Série Vol. 100[114], No. 1/1, pp. 299–304 (2016) 

ABOUT A CONJECTURE ON DIFFERENCE EQUATIONS IN QUASIANALYTIC CARLEMAN CLASSESHicham ZoubeirDepartment of Mathematics, Faculty of Sciences, Ibn Tofail University, Kenitra, MoroccoAbstract: We consider the difference equation ${\sum}_{j=1}^{q}{a}_{j}\left(x\right)\phi (x+{\alpha}_{j})=\chi \left(x\right)$ where ${\alpha}_{1}<\cdots <{\alpha}_{q}$ ($q\ge 3$) are given real constants, ${a}_{j}$ ($j=1,\cdots ,q$) 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 ${C}_{M}\left\{\mathbb{R}\right\}$. We prove, under a growth condition on the functions ${a}_{j}$, that the difference equation above is solvable in ${C}_{M}\left\{\mathbb{R}\right\}$. Keywords: difference equations; quasianalytic Carleman classes Classification (MSC2000): 30H05; 30B10; 30D05 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 8 Nov 2016. This page was last modified: 14 Nov 2016.
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