Integral representations of a class of harmonic functions in the half space
Integral representations of a class of harmonic functions in the half space
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一类调和函数在半空间中的积分表示
DOI：
10.1016/j.jde.2015.09.032
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发表时间：
2016-01
影响因子：
2.4
通讯作者：
Qian, Tao
中科院分区：
文献类型：
--
作者：
Zhang, Yan Hui;Deng, Guan Tie;Qian, Tao
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 parametermdealing with the singularity at the infinity.
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DOI：
--
发表时间：
1971-11
期刊：
--
影响因子：
--
作者：
E. Stein;G. Weiss
通讯作者：
E. Stein;G. Weiss
DOI：
10.1080/02781070412331328602
发表时间：
2005-03
期刊：
Complex Variables, Theory and Application: An International Journal
影响因子：
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作者：
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通讯作者：
Y. Zhang;Guantie Deng
DOI：
10.1017/cbo9780511470950.005
发表时间：
1999-01
期刊：
--
影响因子：
--
作者：
P. Koosis
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P. Koosis
影响因子：
1
作者：
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1.3
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