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On separation of singularities of meromorphic functions. (English. Russian original) Zbl 0611.30032
Math. USSR, Sb. 53, 183-201 (1986); translation from Mat. Sb., Nov. Ser. 125(167), No. 2, 181-198 (1984).
Let E be an arbitrary proper continuum in \({\bar {\mathbb{C}}}\), \(\lambda =\{D_ k\}^ a \)finite collection of bounded pairwise distinct connected components of \({\bar {\mathbb{C}}}\setminus E\), f a function meromorphic in each domain \(D_ k\) and continuous in some neighbourhood of E, \(F_{\lambda}\) be the sum of principal parts of the Laurent expansions of f with respect to the poles in \(\cup D_ k\) and \(n_{\lambda}\) the degree of the rational function \(F_{\lambda}\). The main result of the paper is the inequality \(\| F_{\lambda}\| \leq const\cdot n_{\lambda}\| f\|\) where \(\| \cdot \|\) is the supremum norm on E. Other interesting results concern the case when E is a rectifiable curve.
Reviewer: A.E.Eremenko

MSC:
30E10 Approximation in the complex plane
30A10 Inequalities in the complex plane
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