Vindas, Jasson; Estrada, Ricardo A Tauberian theorem for distributional point values. (English) Zbl 1169.46019 Arch. Math. 91, No. 3, 247-253 (2008). The definition of the value of a distribution at a point was first given by S.Łojasiewicz [Stud.Math.16, 1–36 (1957; Zbl 0086.09405)]. A distribution \(f\in {\mathcal D}'({\mathbb R})\) has the value \(\gamma\) at the point \(x_0\in\mathbb{R}\) if the limit \(\lim_{\varepsilon\to0}f(x_0+\varepsilon x)\) exists in \({\mathcal D}'({\mathbb R})\) and is equal to the constant \(\gamma\). This is denoted by \(f(x_0)=\gamma\).In the present paper, the authors prove that if \(f\in {\mathcal D}'(a,b)\) is the distributional limit of an analytic function \(F\) defined in \((a,b)\times (0,R)\), and \(F(x_0+i y) \to \gamma\) as \(y \to 0^+\), and \(f\) is distributionally bounded at \(x=x_0\), then \(f\) has the value \(\gamma\) at the point \(x_0\). Reviewer: Maria Carmen Fernandez Rosell (Valencia) Cited in 4 Documents MSC: 46F20 Distributions and ultradistributions as boundary values of analytic functions Keywords:Tauberian theory; boundary values of analytic functions; distributional point values Citations:Zbl 0086.09405 PDFBibTeX XMLCite \textit{J. Vindas} and \textit{R. Estrada}, Arch. Math. 91, No. 3, 247--253 (2008; Zbl 1169.46019) Full Text: DOI arXiv