A class of Julia exceptional functions

Abstract

The class of $p$-loxodromic functions (meromorphic functions, satisfying the condition $f(qz) = pf(z)$ for some $q \in \mathbb{C}\backslash \{0\}$ and all $z \in \mathbb{C}\backslash \{0\}$) is studied. Each $p$-loxodromic function is Julia exceptional. The representation of these functions as well as their zero and pole distribution are investigated.

Authors and Affiliations

V. S. Khoroshchak, A. Ya. Khrystiyanyn, D. V. Lukivska

Keywords

Related Articles

ON A COMPLETE TOPOLOGICAL INVERSE POLYCYCLIC MONOID

We give sufficient conditions when a topological inverse l-polycyclic monoid Pl is absolutely Hclosed in the class of topological inverse semigroups. For every infinite cardinal l we construct the coarsest semigroup inve...

On a necessary condition for Lp (0<p<1) -convergence (upper boundedness) of trigonometric series

In this paper we prove that the condition ∑2nk=[n2]λk(p)(|n−k|+1)2−p=o(1)(=O(1)), is a necessary condition for the Lp(0<p<1)-convergence (upper boundedness) of a trigonometric series. Precisely, the results extend some r...

On the intersection of weighted Hardy spaces

Let $H^p_\sigma( \mathbb{C}_+)$, $1\leq p <+\infty$, $0\leq \sigma < +\infty$, be the space of all functions f analytic in the half plane $\mathbb{C}_{+}= \{ z: \text {Re} z>0 \}$ and such that $$ \|f\|:=\sup\limits_{...

Coupled fixed point theorems for weakly compatible mappings along with CLR property in Menger metric spaces

Coupled fixed point problems have attracted much attention in recent times. The aim of this paper is to extend the notions of E.A. property, CLR property and JCLR property for coupled mappings in Menger metric space and...

Paley-Wiener-type theorem for polynomial ultradifferentiable functions

The image of the space of ultradifferentiable functions with compact supports under Fourier-Laplace transformation is described. An analogue of Paley-Wiener theorem for polynomial ultradifferentiable functions is proved.

Download PDF file
  • EP ID EP262989
  • DOI 10.15330/cmp.8.1.172-180
  • Views 72
  • Downloads 0

How To Cite

V. S. Khoroshchak, A. Ya. Khrystiyanyn, D. V. Lukivska (2016). A class of Julia exceptional functions. Карпатські математичні публікації, 8(1), 172-180. https://europub.co.uk/articles/-A-262989