Устранение особенностей и аналоги теоремы Сохоцкого-Вейерштрасса для Q-отображений

Севастьянов, Є. О. (2009) Устранение особенностей и аналоги теоремы Сохоцкого-Вейерштрасса для Q-отображений. Український математичний журнал, 61 (1). pp. 116-126. ISSN 1027-3190

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Abstract

We prove that an open discrete Q-mapping f : D → Rn has a continuous extension to an isolated boundary point if the function Q x ( ) has finite mean oscillation or logarithmic singularities of order at most n – 1 at this point. Moreover, the extended mapping is open and discrete and is a Q-mapping. As a corollary, we obtain an analog of the well-known Sokhotskii–Weierstrass theorem on Q-mappings. In particular, we prove that an open discrete Q-mapping takes any value infinitely many times in the neighborhood of an essential singularity, except, possibly, for a certain set of capacity zero.

Item Type: Article
Subjects: Q Science > QA Mathematics > Mathematical Analysis
Divisions: Faculty of Physics and Mathematics > Department of Mathematical Analysis
Depositing User: Ірина Ігорівна Таргонська
Date Deposited: 10 Nov 2014 09:21
Last Modified: 02 Mar 2017 11:34
URI: http://eprints.zu.edu.ua/id/eprint/13842

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