島根大学総合理工学部紀要.シリーズB

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島根大学総合理工学部紀要.シリーズB 55
2022 発行

POTENTIAL THEORY OF THE DISCRETE EQUATION Δu = qu

KURATA, HISAYASU
山﨑 稀嗣
ファイル
内容記述(抄録等)
We develop a discrete potential theory for the equation Δu = qu on an infinite network similar to the classical potential theory on Riemannian surfaces. The q-Green function for the Schrödinger operator - Δ + q plays the role of the Green function for the Laplace operator. We study some properties of q-Green potential whose kernel is the q-Green function. As an application, we give a classification of infinite networks by the classes of q-harmonic functions.
We also focus on the role of the q-elliptic measure of the ideal boundary of the network.
DOI(SelfDOI)