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

 

Approximation of subharmonic functions


Author: I. Chyzhykov
Translated by: the author
Original publication: Algebra i Analiz, tom 16 (2004), nomer 3.
Journal: St. Petersburg Math. J. 16 (2005), 591-607
MSC (2000): Primary 30A05; Secondary 30D20, 30E10
Published electronically: May 2, 2005
MathSciNet review: 2083571
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Abstract | References | Similar Articles | Additional Information

Abstract: In certain classes of subharmonic functions $u$on $\mathbb C$ distinguished in terms of lower bounds for the Riesz measure of $u$, a sharp estimate is obtained for the rate of approximation by functions of the form $\log \vert f(z)\vert$, where $f$ is an entire function. The results complement and generalize those recently obtained by Lyubarskii and Malinnikova.


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Additional Information

I. Chyzhykov
Affiliation: Faculty of Mechanics and Mathematics, Ivan Franko National University, Lviv, Ukraine
Email: tftj@franko.lviv.ua chyzh@lviv.farlep.net

DOI: http://dx.doi.org/10.1090/S1061-0022-05-00867-8
PII: S 1061-0022(05)00867-8
Received by editor(s): May 12, 2003
Published electronically: May 2, 2005
Additional Notes: Partially supported by the scholarship of the Queen Jadwiga Foundation, Jagellonian University (Kraków, Poland)
Article copyright: © Copyright 2005 American Mathematical Society