  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 $m_1,\cdots,m_t$.
