島根大学総合理工学部紀要.シリーズB

ダウンロード数 : ?
島根大学総合理工学部紀要.シリーズB 54
2021-01-30 発行

DISCRETE MULTI-HARMONIC GREEN FUNCTIONS

KURATA, HISAYASU
山﨑 稀嗣
ファイル
内容記述(抄録等)
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).
DOI(SelfDOI)