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 33
2000-03 発行

Inequalities on Infinite Networks

村上 温
山﨑 稀嗣
ファイル
内容記述(抄録等)
Inequalities on networks have played important roles in the theory of netwoks. We study several famous inequalities on networks such as Wirtinger's inequality, Hardy's inequality, Poincare-Sobolev's inequality and the strong isoperimetric inequality, etc. These inequalities are closely related to the smallest eigenvalue of weighted discrete Laplacian. We discuss some relations between these inequalities and the potential-theorerteic magnitude of the ideal boundary of an infinite network.