Geodesic
Characterization of functions whose forward differences are exponential polynomials
Commentationes Mathematicae Universitatis Carolinae, Tome 58 (2017) no. 4, pp. 435-442.

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Given $\{h_1,\cdots,h_{t}\}$ a finite subset of $\mathbb{R}^d$, we study the continuous complex valued functions and the Schwartz complex valued distributions $f$ defined on $\mathbb{R}^d$ with the property that the forward differences $\Delta_{h_k}^{m_k}f$ are (in distributional sense) continuous exponential polynomials for some natural numbers $m_1,\cdots,m_t$.
DOI : 10.14712/1213-7243.2015.224
Classification : 39A70, 39B52
Keywords: functional equations; exponential polynomials; generalized functions; forward differences 
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Almira, J. M. Characterization of functions whose forward differences are exponential polynomials. Commentationes Mathematicae Universitatis Carolinae, Tome 58 (2017) no. 4, pp. 435-442. doi : 10.14712/1213-7243.2015.224. http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2015.224/

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