Composition, product and sum of analytic functions of bounded L-index in direction in the unit ball
Journal Title: Математичні Студії - Year 2018, Vol 50, Issue 2
Abstract
In this paper, we investigate a composition of entire function of one variable and analytic function in the unit ball. There are obtained conditions which provide equivalence of bounded\-ness of L-index in a direction for such a composition and boundedness of l-index of initial function of one variable, where the continuous function L:Bn→R+ is constructed by the continuous function l:C→R+. We present sufficient conditions for boundedness of L-index in the direction for sum and for product of functions analytic in the unit ball. The class of analytic functions in the unit ball having bounded L-index in direction is very wide because it contains all analytic functions with bounded multiplicities of zeros on every complex line {z0+tb:t∈C}. It is a statement of proved existence theorem. In the one-dimensional case these results are new for functions analytic in the unit disc.
Authors and Affiliations
Andriy Bandura
Keywords
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- EP ID EP525256
- DOI 10.15330/ms.50.2.115-134
- Views 63
- Downloads 0
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