UM
Integral representations of a class of harmonic functions in the half space
Yan Hui Zhang1,2; Guan Tie Deng3; Tao Qian4
2016
Source PublicationJournal of Differential Equations
ISSN10902732 00220396
Volume260Issue:2Pages:923-936
Abstract

In this article, motivated by the classic Hadamard factorization theorem about an entire function of finite order in the complex plane, we firstly prove that a harmonic function whose positive part satisfies some growth conditions, can be represented by its integral on the boundary of the half space. By using Nevanlinna's representation of harmonic functions and the modified Poisson kernel of the half space, we further prove a representation formula through integration against a certain measure on the boundary hyperplane for harmonic functions not necessarily continuous on the boundary hyperplane whose positive parts satisfy weaker growing conditions than the first question. The result is further generalized by involving a parameter m dealing with the singularity at the infinity.

KeywordIntegral Representation Modified Poisson Kernel Positive Part
DOIhttp://doi.org/10.1016/j.jde.2015.09.032
URLView the original
Indexed BySCI
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics
WOS IDWOS:000373536400001
Fulltext Access
Citation statistics
Cited Times [WOS]:5   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionUniversity of Macau
Corresponding AuthorYan Hui Zhang
Affiliation1.Department of Mathematics, Beijing Technology and Business University, Beijing 100048, China
2.Department of Statistics, University College Cork, Cork, Ireland
3.School of Mathematical Sciences, Key Laboratory of Mathematics and Complex Systems of Ministry of Education, Beijing Normal University, 100875, Beijing, China
4.Department of Mathematics, Faculty of Science and Technology, University of Macau, Macau (Via Hong Kong)
Recommended Citation
GB/T 7714
Yan Hui Zhang,Guan Tie Deng,Tao Qian. Integral representations of a class of harmonic functions in the half space[J]. Journal of Differential Equations,2016,260(2):923-936.
APA Yan Hui Zhang,Guan Tie Deng,&Tao Qian.(2016).Integral representations of a class of harmonic functions in the half space.Journal of Differential Equations,260(2),923-936.
MLA Yan Hui Zhang,et al."Integral representations of a class of harmonic functions in the half space".Journal of Differential Equations 260.2(2016):923-936.
Files in This Item:
There are no files associated with this item.
Related Services
Recommend this item
Bookmark
Usage statistics
Export to Endnote
Google Scholar
Similar articles in Google Scholar
[Yan Hui Zhang]'s Articles
[Guan Tie Deng]'s Articles
[Tao Qian]'s Articles
Baidu academic
Similar articles in Baidu academic
[Yan Hui Zhang]'s Articles
[Guan Tie Deng]'s Articles
[Tao Qian]'s Articles
Bing Scholar
Similar articles in Bing Scholar
[Yan Hui Zhang]'s Articles
[Guan Tie Deng]'s Articles
[Tao Qian]'s Articles
Terms of Use
No data!
Social Bookmark/Share
All comments (0)
No comment.
 

Items in the repository are protected by copyright, with all rights reserved, unless otherwise indicated.