On a complete description of the class of functions without zeros analytic in a disk and having given orders

  • I. E. Chyzhykov.

Abstract

For arbitrary $0 ≤ σ ≤ ρ ≤ σ + 1$, we describe the class $A_{σ}^{ρ}$ of functions $g(z)$ analytic in the unit disk $D = \{z : ∣z∣ < 1\}$ and such that $g(z) ≠ 0,\; ρ_T[g] = σ$, and $ρ_M[g] = ρ$, where $M(r,g) = \max \{|g(z)|:|z|⩽r\},\quad$ $T(r,u) = \cfrac1{2π} ∫_0^{2π} ln^{+}|g(re^{iφ})|dφ,\quad$ $ρ_M[g] = \lim \sup_{r↑1} \cfrac{lnln^{+}M(r,g)}{−ln(1−r)},$ $\quad ρT[g] = \lim \sup_{r↑1} \cfrac{ln^{+}T(r,g)}{−ln(1−r)}$.
Published
25.07.2007
How to Cite
Chyzhykov.I. E. “On a Complete Description of the Class of Functions Without Zeros Analytic in a Disk and Having Given Orders”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, no. 7, July 2007, pp. 979–995, https://umj.imath.kiev.ua/index.php/umj/article/view/3360.
Section
Research articles