Characterization of distributions whose forward differences are exponential polynomials

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 $m_1,\cdots ,m_t$.

10 pages, submitted to a Journal. arXiv admin note: substantial text overlap with arXiv:1612.03756

Cited by in corpus (1)

• A Montel-type theorem for mixed differences