caa a22 4500 475741889 CHVBK 20180406123501.0 cr unu---uuuuu 170329e20000401xx s 000 0 eng 10.1007/BF02676401 doi (NATIONALLICENCE)springer-10.1007/BF02676401 Korobeinik Yu Rostov State University, USSR aut Analytic solutions of the Borel problem [Elektronische Daten] [Yu. Korobeinik] LetF ⊂ ℂ be a dense-in-itself set that has a nonempty connected interior and contains the origin, and let $$C^\infty (\mathcal{F})$$ be the space of infinitely differentiable complex-valued functions onF. For some classes of such setsF, we prove that for an arbitrary sequence $$\left\{ {d_n } \right\}_{n = 0}^\infty $$ of complex numbers there exists a functionf ε $$C^\infty (\mathcal{F})$$ withf (n)(0)=d n,n=0, 1, 2, ..., and study the analyticity properties off. The functionf is constructed in the form of various function series, namely, a power series, a series of simple fractions, and an exponential series. Analytic solutions of the multidimensional Borel problem are also considered. Kluwer Academic/Plenum Publishers, 2000 Borel problem nationallicence analytic solution nationallicence B -set nationallicence domain of existence nationallicence singular point nationallicence power series nationallicence exponential series nationallicence simple fraction nationallicence Mathematical Notes Kluwer Academic Publishers-Plenum Publishers 67/4(2000-04-01), 448-458 0001-4346 67:4<448 2000 67 11006 https://doi.org/10.1007/BF02676401 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02676401 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Korobeinik Yu Rostov State University, USSR aut NATIONALLICENCE 773 0- Mathematical Notes Kluwer Academic Publishers-Plenum Publishers 67/4(2000-04-01), 448-458 0001-4346 67:4<448 2000 67 11006 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer