| ファイル情報(添付) | |
| タイトル |
POTENTIAL THEORY OF THE DISCRETE EQUATION Δu = qu
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| 著者 | |
| 収録物名 |
島根大学総合理工学部紀要.シリーズB
Memoirs of the Graduate School of Science and Engineering, Shimane University. Series B, Mathematics
|
| 巻 | 55 |
| 開始ページ | 1 |
| 終了ページ | 25 |
| 収録物識別子 |
ISSN 1342-7121
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| 内容記述 |
抄録・要旨
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. |
| 主題 |
discrete potential theory
classification of infinite networks
Schr¨odinger operator
q-Green potential
discrete q-Laplacian
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| 言語 |
英語
|
| 資源タイプ | 紀要論文 |
| 出版者 |
総合理工学部
The Interdisciplinary Graduate School of Science and Engineering
|
| 発行日 | 2022 |
| 出版タイプ | Version of Record（出版社版。早期公開を含む） |
| アクセス権 | オープンアクセス |
| 関連情報 |
ソウゴウ リコウ ガクブ
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