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language
eng
Author
KURATA, HISAYASU
YAMASAKI, MARETSUGU
Description
The harmonic Green function ga of an infinite network defined as the unique Dirichlet potential which satisfies Δga = −δa. The biharmonic Green function ga(2) (x) is defined by the convolution of gx and ga in [6]. It is known that Δ2ga(2) = δa if ga(2) is finite and that ga(2) is a Dirichlet potential if ga has a finite Green energy. In this paper, we define the k-harmonic Green function ga(k) (x) as the convolution of gx(k−1) and ga if it converges. We study some potential theoretic properties related to ga(k).
Journal Title
Memoirs of the Graduate School of Science and Engineering, Shimane University. Series B, Mathematics
Volume
54
Start Page
1
End Page
14
ISSN
1342-7121
Published Date
2021-01-30
Publisher
総合理工学部
Publisher Aalternative
The Interdisciplinary Graduate School of Science and Engineering
NII Type
Departmental Bulletin Paper
Format
PDF
Text Version
出版社版
OAI-PMH Set
Faculty of Science and Engineering
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