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

Author
M. Ya. Kravets
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
Riemann-Liouville fractional integral operator; analytic function in the unit disc; order of growth; harmonic function
DOI
doi:10.15330/ms.45.1.27-33
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), 3544.

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, 4, (2013), 12971311.

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), 1, 5364.

4. I.E. Chyzhykov, Growth and representation of analytic and harmonic functions in the unit disc, Ukr. Mat. Bull., 29, 1, (2006), 3144.

5. . Zygmund, Trigonometrical Series, Warsaw, 1935.

6. A. Grishin, Continuity and asymptotic continuity of subharmonic functions, Math. Physics, Analysis, Geometry, ILPTE, V.1, 1994, 2, 193215.

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), 7, 10881109.

Pages
27-33
Volume
45
Issue
1
Year
2016
Journal
Matematychni Studii
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