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