Characterization of functions whose forward differences are exponential polynomials

Commentationes mathematicae Universitatis Carolinae

J. M. Almira

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

DOI  :  10.14712/1213-7243.2015.224

学科分类：物理化学和理论化学

来源: Univerzita Karlova v Praze * Matematicko-Fyzikalni Fakulta / Charles University in Prague, Faculty of Mathematics and Physics

【 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 $m_1,\\cdots,m_t$.

【 授权许可】

CC BY