Characterization of functions whose forward differences are exponential polynomials

[摘要] 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 $m_1,\\cdots,m_t$.

[学科分类] 物理化学和理论化学

[关键词] functional equations;exponential polynomials;generalized functions;forward differencesDOI: DOI 10.14712/1213-7243.2015.224AMS Subject Classification: 39A70 39B52 PDF