Universally prestarlike functions as convolution multipliers

作     者：Ruscheweyh, Stephan Salinas, Luis 

作者机构：Univ Wurzburg Math Inst D-97074 Wurzburg Germany Univ Tecn F Santa Maria Dept Informat Valparaiso Chile 

出 版 物：《MATHEMATISCHE ZEITSCHRIFT》 (数学杂志)

年 卷 期：2009年第263卷第3期

页      面：607-617页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：FONDECYT [1070269, 7080064] DGIP-UTFSM German-Israeli Foundation [G-809-234.6/2003] 

主　　题：Universally prestarlike functions Universally convex functions Convolution invariance Bernardi-Libera transform 

摘      要：Universally prestarlike functions (of order alpha = 1) in the slit domain Lambda := C\[1, infinity] have recently been introduced in Ruscheweyh et al. (Israel J Math, to appear). This notation generalizes the corresponding one for functions in the unit disk D (and other circular domains in C). In this paper we study the behaviour of universally prestarlike functions under the Hadamard product. In particular it is shown that these function classes (with alpha fixed), are closed under convolution, and that their members, as Hadamard multipliers, also preserve the prestarlikeness (of the same order) of functions in arbitrary circular domains containing the origin.