| File | |
| Title |
POTENTIAL THEORY OF THE DISCRETE EQUATION Δu = qu
|
| Creator | |
| Source Title |
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
|
| Volume | 55 |
| Start Page | 1 |
| End Page | 25 |
| Journal Identifire |
ISSN 1342-7121
|
| Descriptions |
Abstract
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. |
| Subjects |
discrete potential theory
classification of infinite networks
Schr¨odinger operator
q-Green potential
discrete q-Laplacian
|
| Language |
eng
|
| Resource Type | departmental bulletin paper |
| Publisher |
総合理工学部
The Interdisciplinary Graduate School of Science and Engineering
|
| Date of Issued | 2022 |
| Publish Type | Version of Record |
| Access Rights | open access |
| Relation |
ソウゴウ リコウ ガクブ
|
