Composition of entire functions and bounded L-index in direction
Journal Title: Математичні Студії - Year 2017, Vol 47, Issue 2
Abstract
In the present paper we give an answer to the following question: Let f:C→C be an entire function of bounded l-index, Φ:Cn→C be an entire function, n≥2, l:C→R+ be a continuous function. What are a positive continuous function L:Cn→R+ and a direction b∈Cn∖{0} such that the composite function f(Φ(z)) has bounded L-index in the direction b?
Authors and Affiliations
Andriy Bandura
Keywords
Related Articles
- EP ID EP310109
- DOI 10.15330/ms.47.2.179-184
- Views 38
- Downloads 0
Distance between a maximum modulus point and zero set of an analytic function
Let f be an analytic function in the disk DR={z∈C:|z|≤R}, R∈(0,+∞]. We call a point w∈DR a maximum modulus point of f if |f(w)|=M(|w|,f), where M(r,f)=max{|f(z)|:|z|=r}. Denote by d(w,f) the distance between a maximum mo...
About some problem for entire functions of unbounded index in any direction
In this paper, we select a class of entire functions F(z1,…,zn) such that for any direction (b1,…,bn)∈Cn∖{0} and for every point (z01,…,z0n)∈C the function F(z01+tb1,…,z0n+tbn) is of bounded index as a function in variab...
The algebra of symmetric polynomials on (L∞)n
The paper deals with continuous symmetric (invariant under composition of the variable with any measure preserving bijection of [0,1]) complex-valued polynomials on the nth Cartesian power of the complex Banach space L∞...
On the l-index boundedness of some composition of functions
It is suggested that for an entire function f the function F(z)=f(q(1−z)n), n∈N, is of bounded l-index with l(|z|)=β(1−|z|)n+1, β>1, if and only if f is of bounded index.
Note on separately symmetric polynomials on the Cartesian product of ℓ1
In the paper, we describe algebraic bases in algebras of separately symmetric polynomials which are defined on Cartesian products of n copies of ℓ1. Also, we describe spectra of algebras of entire functions, generated by...