Vector-valued holomorphic and harmonic functions

IF 0.3 Q4 MATHEMATICS Concrete Operators Pub Date : 2016-04-28 DOI:10.1515/conop-2016-0007
W. Arendt
{"title":"Vector-valued holomorphic and harmonic functions","authors":"W. Arendt","doi":"10.1515/conop-2016-0007","DOIUrl":null,"url":null,"abstract":"Abstract Holomorphic and harmonic functions with values in a Banach space are investigated. Following an approach given in a joint article with Nikolski [4] it is shown that for bounded functions with values in a Banach space it suffices that the composition with functionals in a separating subspace of the dual space be holomorphic to deduce holomorphy. Another result is Vitali’s convergence theorem for holomorphic functions. The main novelty in the article is to prove analogous results for harmonic functions with values in a Banach space.","PeriodicalId":53800,"journal":{"name":"Concrete Operators","volume":"3 1","pages":"68 - 76"},"PeriodicalIF":0.3000,"publicationDate":"2016-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/conop-2016-0007","citationCount":"10","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Concrete Operators","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/conop-2016-0007","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 10

Abstract

Abstract Holomorphic and harmonic functions with values in a Banach space are investigated. Following an approach given in a joint article with Nikolski [4] it is shown that for bounded functions with values in a Banach space it suffices that the composition with functionals in a separating subspace of the dual space be holomorphic to deduce holomorphy. Another result is Vitali’s convergence theorem for holomorphic functions. The main novelty in the article is to prove analogous results for harmonic functions with values in a Banach space.
查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
向量值全纯函数与调和函数
研究了Banach空间中带值的全纯函数和调和函数。根据与Nikolski[4]的联合文章给出的方法,证明了对于在Banach空间中有值的有界函数,在对偶空间的分离子空间中与泛函的复合是全纯的就足以推导出全纯。另一个结果是全纯函数的Vitali收敛定理。本文的主要新颖之处在于证明了巴拿赫空间中带值调和函数的类似结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 去求助
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
期刊最新文献
On the compactness and the essential norm of operators defined by infinite tridiagonal matrices m-Isometric tensor products Estimation of coefficient bounds for a subclass of Sakaguchi kind functions mapped onto various domains Generalized Crofoot transform and applications Generalized Hausdorff operator on Bergmann spaces
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1