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St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)

 
 

 

Subsequences of zeros for classes of holomorphic functions, their stability, and the entropy of arcwise connectedness. II


Authors: B. N. Khabibullin, F. B. Khabibullin and L. Yu. Cherednikova
Translated by: S. Kislyakov
Original publication: Algebra i Analiz, tom 20 (2008), nomer 1.
Journal: St. Petersburg Math. J. 20 (2009), 131-162
MSC (2000): Primary 30C15
DOI: https://doi.org/10.1090/S1061-0022-08-01041-8
Published electronically: November 14, 2008
MathSciNet review: 2411973
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Abstract: Let $ \Omega$ be a domain in the complex plane $ \mathbb{C}$, $ H(\Omega)$ the space of functions holomorphic in $ \Omega$, and $ \mathscr{P}$ a family of functions subharmonic in $ \Omega$. Denote by $ H_{\mathscr{P}}(\Omega )$ the class of functions $ f\in H(\Omega)$ satisfying $ \vert f(z)\vert\leq C_f\exp p_f(z)$ for all $ z\in \Omega$, where $ p_f \in \mathscr{P}$ and $ C_f$ is a constant. Conditions are found ensuring that a sequence $ \Lambda =\{\lambda_k\} \subset \Omega$ be a subsequence of zeros for various classes $ H_{\mathscr{P}}(\Omega )$. As a rule, the results and the method are new already when $ \Omega=\mathbb{D}$ is the unit circle and $ \mathscr{P}$ is a system of radial majorants $ p(z)=p(\vert z\vert)$.


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Additional Information

B. N. Khabibullin
Affiliation: Bashkir State University, Institute of Mathematics with Computer Center, Urals Scientific Center, Russian Academy of Sciences, Ufa, Bashkortostan, Russia
Email: khabib-bulat@mail.ru

F. B. Khabibullin
Affiliation: Bashkir State University, Institute of Mathematics with Computer Center, Urals Scientific Center, Russian Academy of Sciences, Ufa, Bashkortostan, Russia

L. Yu. Cherednikova
Affiliation: Bashkir State University, Institute of Mathematics with Computer Center, Urals Scientific Center, Russian Academy of Sciences, Ufa, Bashkortostan, Russia

DOI: https://doi.org/10.1090/S1061-0022-08-01041-8
Keywords: Holomorphic function, algebra of functions, weighted space, nonuniqueness sequence
Received by editor(s): November 8, 2006
Published electronically: November 14, 2008
Additional Notes: Supported by RFBR, grant no. 06-01-00067, and by the Program of state subventions for leading scientific schools, grant NSh-10052.2006.1
Article copyright: © Copyright 2008 American Mathematical Society

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