Grzybowski, Jerzy Analytic continuation from compact set. (English) Zbl 0664.32009 Zesz. Nauk. Uniw. Jagielloń. 860, Acta Math. 27, 259-269 (1988). Let K be a compact set in \(K^ n={\mathbb{R}}^ n\) or \({\mathbb{C}}^ n\) and let A(K) be a space of germs on K of all functions analytic near K. For a point \(x\in K\) and germ \(f_ K\) in A(K) let \(T_ xf_ K\) denote the power series expansion at the point x of germ \(f_ K\) whose radius of convergence is \(r(T_ xf_ K)\). Let further, for \(R>0\) \[ A_ R(K)=\{f_ K\in A(K):\quad r(T_ xf_ K)\geq R,\quad \forall x\in K\}. \] We say that a compact K has the extension property if for every \(R>0\) exist an open neighbourhood \(U_ k\) of K such that \(A_ R(K)\subset A(U_ R).\) Using the geometric approach the author proofs the following theorems: Theorem 3.1. Every continuum \(K\subset R^ 2\) has the extension property. Theorem 4.2. Every L-connected (in sense of Zame) continuum \(K\subset K^ n\) has the extension property. These results permits to the author to obtain in a unified manner the results of G. T. Varfolomeev, W. R. Zame and J. T. Rogers. Reviewer: N.I.Skiba MSC: 32D15 Continuation of analytic objects in several complex variables Keywords:analytic functions; analytic continuation; compact set PDFBibTeX XMLCite \textit{J. Grzybowski}, Zesz. Nauk. Uniw. Jagielloń. [...], Acta Math. 860(27), 259--269 (1988; Zbl 0664.32009)