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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Zero distribution and factorization of analytic functions of slow growth in the unit disc


Author: I. Chyzhykov
Journal: Proc. Amer. Math. Soc. 141 (2013), 1297-1311
MSC (2010): Primary 30J99; Secondary 30D35, 30H15, 37A45
Published electronically: August 21, 2012
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Abstract: For a meromorphic function $ f$ in the unit disc, let the $ \rho _\infty $-order of the growth be the limit of the orders of $ L_p$-norms of $ \log \vert f(re^{i\theta })\vert$ over the circle. In the case when the order of the maximum modulus function is smaller than 1, we describe zero distribution of canonical products and derive a new factorization theorem and logarithmic derivative estimates.


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Additional Information

I. Chyzhykov
Affiliation: Faculty of Mechanics and Mathematics, Ivan Franko National University of Lviv, Universytets’ka 1, 79000, Lviv, Ukraine
Email: chyzhykov@yahoo.com

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11463-7
PII: S 0002-9939(2012)11463-7
Keywords: Analytic function, factorization, zero distribution, canonical product, proximate order, order of growth, logarithmic derivative
Received by editor(s): May 9, 2011
Received by editor(s) in revised form: August 9, 2011
Published electronically: August 21, 2012
Communicated by: Mario Bonk
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.