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 51
2018-03 発行

DISCRETE q-GREEN POTENTIALS WITH FINITE ENERGY

Kurata, Hisayasu
山﨑 稀嗣
ファイル
内容記述(抄録等)
Discrete q-Green potentials related to the equation Δu􀀀qu = 0 on an in nite network were studied in [12] as a discrete analogue to [9]. We study some properties of q-Green potentials with nite q-Green energy. The q-Dirichlet energy plays an important role instead of the Dirichlet sum. Our aim is to show that results obtained in [7] in case q = 0 hold similarly even in case q  0. We show that every q-Dirichlet potential can be expressed as a difference of two q-Green potentials with nite q-Green energy.