Author:
Borodin P. A.,Shklyaev K. S.
Abstract
Abstract
For unbounded simply connected domains
in the complex plane, bounded by several simple curves with regular asymptotic behaviour at infinity, we obtain necessary conditions and sufficient conditions for simple partial fractions (logarithmic derivatives of polynomials) with poles on the boundary of
to be dense in the space of holomorphic functions in
(with the topology of uniform convergence on compact subsets of
). In the case of a strip
bounded by two parallel lines, we give estimates for the convergence rate to zero in the interior of
of simple partial fractions with poles on the boundary of
and with one fixed pole.
Bibliography: 16 titles.
Funder
Russian Foundation for Basic Research
Ministry of Education and Science of the Russian Federation
Subject
Algebra and Number Theory
Cited by
5 articles.
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