2017
Том 69
№ 7

All Issues

Removal of singularities and analogs of the Sokhotskii–Weierstrass theorem for Q-mappings

Sevost'yanov E. A.

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Abstract

We prove that an open discrete Q-mapping \( f:D \to \overline {{\mathbb{R}^n}} \) 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.

English version (Springer): Ukrainian Mathematical Journal 61 (2009), no. 1, pp 140-153.

Citation Example: Sevost'yanov E. A. Removal of singularities and analogs of the Sokhotskii–Weierstrass theorem for Q-mappings // Ukr. Mat. Zh. - 2009. - 61, № 1. - pp. 116-126.

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