On the l-index boundedness of some composition of functions
Journal Title: Математичні Студії - Year 2017, Vol 47, Issue 2
Abstract
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.
Authors and Affiliations
Myroslav Sheremeta
Keywords
Related Articles
- EP ID EP310129
- DOI 10.15330/ms.47.2.207-210
- Views 36
- 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...
On uniqueness of entropy solutions for nonlinear elliptic degenerate anisotropic equations
In the present paper we deal with the Dirichlet problem for a class of degenerate anisotropic elliptic second-order equations with L1-right-hand sides in a bounded domain of Rn (n⩾2). This class is described by the prese...
On generalized preopen sets
Firstly in this paper, we find some conditions under which μ-preopen sets of a GTS or μ-space X may be equivalent to μ-open in X. Finally, we obtain some characterizations of generalized paracompactness of a GTS or μ-spa...
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...
Dual pair of eigenvalues in rank one singular nonsymmetric perturbations
In the separable Hilbert space, we discuss the eigenvalue problem for a rank one singular nonselfadjoint perturbation of a selfadjoint operator A, by nonsymmetric potential (δ1≠δ2) in the form A~=A+α⟨⋅,δ1⟩δ2. We give the...