Tests for certain rational functions to belong to the class \(K_ n(D)\)
type: Item
instance of: scholarly article
title: Tests for certain rational functions to belong to the class \(K_ n(D)\)
zbMATH Open document ID: 0542.30017
DOI: 10.1007/BF00966617
author: E. G. Kiryatzkii
author: I. B. Melyauskas
published in: Lithuanian Mathematical Journal
publication date: 1983-01-01T00:00:00Z
review text: Let D be a domain in \({\mathbb{C}}\) and n a natural number. Then a single valued function F(z) is said to belong to the class \(K_ n(D)\) if it is holomorphic in D and the n-th divided difference \([F(z);z_ 0z_ 1...z_ n]\) is not equal to zero for any \(z_ 0,z_ 1,...,z_ n\in D.\) It is noticed that \(K_ 1(D)\) is the set of all holomorphic schlicht functions. In this paper, the authors give various kinds of necessary and sufficient conditions for some simple rational functions to belong to the class \(K_ n(D)\) where D is the unit disk E or a sector \(U_ p=\{z\in {\mathbb{C}}| | \arg z|<\pi /(p+1)\}.\)
Mathematics Subject Classification ID: 30C55
Mathematics Subject Classification ID: 30E99
zbMATH DE Number: 3861511
zbMATH Keywords: n-th divided difference
zbMATH Keywords: rational functions
reviewed by: Kyoichi Takano
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3861511