J. M. Almira
Characterization of functions whose forward differences are exponential polynomials

Comment.Math.Univ.Carolin. 58,4 (2017) 435-442.

Abstract: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 $m_1,\cdots,m_t$.

Keywords: functional equations; exponential polynomials; generalized functions; forward differences

DOI: DOI 10.14712/1213-7243.2015.224
AMS Subject Classification: 39A70 39B52