To problem of description of analytic functions in the unit disk with prescribed orders (in Ukrainian) 

Author 
marjana_s@ukr.net
Ivan Franko National University of Lviv

Abstract 
In two particular cases it is proved I. E. Chyzhykov's conjecture on the representation of
analytic functions in the unit disk with prescribed values of orders.

Keywords 
RiemannLiouville fractional integral operator; analytic function in the unit disc; order of growth;
harmonic function

DOI 
doi:10.15330/ms.45.1.2733

Reference 
1. I.E. Chyzhykov, Growth of analytic functions in the unit disc and complete measure in the sense of
Grishin, Mat. Stud., 29 (2008), 35–44.
2. I.E. Chyzhykov, Zero distribution and factorization of analytic functions of slow growth in the unit disc, Proc. of the Amer. Math. Soc., 141, ¹4, (2013), 1297–1311. 3. I. Chyzhykov, M. Kravets, On the minimum modulus of analytic functions of moderate growth in the unit disc, Comput. Methods Funct. Theory, 16 (2016), ¹1, 53–64. 4. I.E. Chyzhykov, Growth and representation of analytic and harmonic functions in the unit disc, Ukr. Mat. Bull., 29, ¹1, (2006), 31–44. 5. À. Zygmund, Trigonometrical Series, Warsaw, 1935. 6. A. Grishin, Continuity and asymptotic continuity of subharmonic functions, Math. Physics, Analysis, Geometry, ILPTE, V.1, 1994, ¹2, 193–215. 7. M.M. Djrbashian, Integral transformations and representation of functions in a complex domain, M: Nauka, Moscow, 1966. (in Russian) 8. I.E. Chyzhykov, Approximation of subharmonic functions by analytic ones and asymptotic properties of meromorphic functions in a disc: Doctor of sciences thesis, Lviv, 2008. 9. I.E. Chyzhykov, On a complete description of the class of functions without zeros analytic in a disk and having given orders, Ukrainian Math. J., 59 (2007), ¹7, 1088–1109. 
Pages 
2733

Volume 
45

Issue 
1

Year 
2016

Journal 
Matematychni Studii

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