Towards a theory of removable singularities for maps with unbounded characteristic of quasi-conformity
Zhytomyr State University Library
Переглянути архів Інформація| Поле | Співвідношення | |
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http://eprints.zu.edu.ua/13934/
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| Title |
Towards a theory of removable singularities for maps with unbounded characteristic of quasi-conformity |
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| Creator |
Sevost’yanov, Е. А.
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| Subject |
Mathematical Analysis
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| Description |
We prove that sets of zero modulus with weight Q (in particular, isolated singularities) are removable for discrete open Q-maps f: D ! Rn if the function Q(x) has finite mean oscillation or a logarithmic singularity of order not exceeding n − 1 on the corresponding set. We obtain analogues of the well-known Sokhotskii–Weierstrass theorem and also of Picard’s theorem. In particular, we show that in the neighbourhood of an essential singularity, every discrete open Q-map takes any value infinitely many times, except possibly for a set of values of zero capacity. |
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| Publisher |
Національна академія наук
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| Date |
2010
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| Type |
Article
PeerReviewed |
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| Format |
text
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| Language |
uk
english |
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| Identifier |
http://eprints.zu.edu.ua/13934/1/Izvestiya_Mathematics.pdf
Sevost’yanov, Е. А. (2010) Towards a theory of removable singularities for maps with unbounded characteristic of quasi-conformity. Mathematics Sabject Classsfication (74). pp. 151-165. ISSN 1027-3190 |
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