caa a22 4500 475740327 CHVBK 20180406123458.0 cr unu---uuuuu 170329e20000701xx s 000 0 eng 10.1007/BF02674640 doi (NATIONALLICENCE)springer-10.1007/BF02674640 A generalization of the Laurent series [Elektronische Daten] [A. Abanin, G. Semenova] We study conditions on a domainG in the extended complex plane $$\widehat{\mathbb{C}}$$ and a sequence $$\Lambda = \left\{ {\lambda _k } \right\}$$ of points in the complement $$G^c = \widehat{\mathbb{C}}\backslash G$$ ofG under which every functionf(z) holomorphic inG and vanishing atz=∞ (if ∞∈G) admits a representation (possibly, nonunique) by a series 1 $$f\left( z \right) = \mathop \sum \limits_{k = 1}^\infty \mathop \sum \limits_{j = 1}^\infty \frac{{a_{k,j} }}{{\left( {z - \lambda _k } \right)j}},$$ which is uniformly and absolutely convergent in the interior ofG. For the case in which $$ \bar G \subset {\mathbb{C}} $$ or $$G^c \subset {\mathbb{C}}$$ , this expansion exists if and only if the system $$\{ K(\lambda _k $$ , of disks covers ∂G for each ε>0. Kluwer Academic/Plenum Publishers, 2000 analytic function of one complex variable nationallicence series representation nationallicence laurent series nationallicence simple fraction nationallicence locally convex space nationallicence Fréchet space nationallicence absolutely representing system nationallicence Abanin A. Rostov State University, USSR aut Semenova G. Rostov State University, USSR aut Mathematical Notes Springer Netherlands 68/1(2000-07-01), 3-11 0001-4346 68:1<3 2000 68 11006 https://doi.org/10.1007/BF02674640 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02674640 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Abanin A. Rostov State University, USSR aut NATIONALLICENCE 700 1- Semenova G. Rostov State University, USSR aut NATIONALLICENCE 773 0- Mathematical Notes Springer Netherlands 68/1(2000-07-01), 3-11 0001-4346 68:1<3 2000 68 11006 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer