Transcendental operators acting on slice regular functions

IF 0.3 Q4 MATHEMATICS
C. de Fabritiis
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引用次数: 0

Abstract

Abstract The aim of this paper is to carry out an analysis of five trascendental operators acting on the space of slice regular functions, namely *-exponential, *-sine and *-cosine and their hyperbolic analogues. The first three of them were introduced by Colombo, Sabadini and Struppa and some features of *-exponential were investigated in a previous paper by Altavilla and the author. We show how exp*(f ), sin*(f ), cos*(f ), sinh*(f ) and cosh*(f ) can be written in terms of the real and the vector part of the function f and we examine the relation between cos* and cosh* when the domain Ω is product and when it is slice. In particular we prove that when Ω is slice, then cos*(f ) = cosh*(f * I) holds if and only if f is ℂI preserving, while in the case Ω is product there is a much larger family of slice regular functions for which the above relation holds.
作用于切片正则函数的超越算子
摘要本文的目的是分析作用于切片正则函数空间上的五种逆算子,即*-指数、*-正弦和*-余弦及其双曲类似物。其中前三种是由Colombo, Sabadini和Struppa介绍的,而Altavilla和作者在之前的文章中研究了*-指数的一些特征。我们展示了exp*(f), sin*(f), cos*(f), sinh*(f)和cosh*(f)如何可以用函数f的实部和向量部来表示,并且我们检查了当定义域Ω是积和切片时cos*和cosh*之间的关系。特别地,我们证明了当Ω是切片时,当且仅当f是守恒的,那么cos*(f) = cosh*(f * I)成立,而当Ω是乘积时,存在一个更大的切片正则函数族,其中上述关系成立。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Concrete Operators
Concrete Operators MATHEMATICS-
CiteScore
1.00
自引率
16.70%
发文量
10
审稿时长
22 weeks
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