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St. Petersburg Mathematical Journal
St. Petersburg Mathematical Journal
ISSN 1547-7371(online) ISSN 1061-0022(print)

On uniform approximation of harmonic functions


Author: M. Ya. Mazalov
Translated by: S. Kislyakov
Original publication: Algebra i Analiz, tom 23 (2011), nomer 4.
Journal: St. Petersburg Math. J. 23 (2012), 731-759
MSC (2010): Primary 31B15, 31B05; Secondary 41A63
Published electronically: April 13, 2012
MathSciNet review: 2893523
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Abstract: The paper is devoted to uniform approximation by harmonic functions on compact sets. The result is an approximation theorem for an individual function under the condition that, on the complement to the compact set, the harmonic capacity is ``homogeneous'' in a sense. The proof involves a refinement of Vitushkin's localization method.


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Additional Information

M. Ya. Mazalov
Affiliation: USSR Marshal A. M. Vasilevskiĭ Military Academy of Air Defence, Military Forces of RF, Ul. Kotovskogo 2, Smolensk 214027, Russia
Email: maksimmazalov@yandex.ru

DOI: http://dx.doi.org/10.1090/S1061-0022-2012-01215-X
PII: S 1061-0022(2012)01215-X
Keywords: Uniform approximation, harmonic functions, capacities, singular integrals, Carleson measures
Received by editor(s): March 15, 2010
Published electronically: April 13, 2012
Additional Notes: Supported in part by the grant NSh-3476.2010.1 for support of leading scientific schools
Article copyright: © Copyright 2012 American Mathematical Society