| File | |
| language |
eng
|
| Author |
KURATA, HISAYASU
YAMASAKI, MARETSUGU
|
| Description | 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. |
| Subject | discrete potential theory
classification of infinite networks
Schr¨odinger operator
q-Green potential
discrete q-Laplacian
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| Journal Title |
Memoirs of the Graduate School of Science and Engineering, Shimane University. Series B, Mathematics
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| Volume | 55
|
| Start Page | 1
|
| End Page | 25
|
| ISSN | 1342-7121
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| Published Date | 2022
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| Publisher | 総合理工学部
|
| Publisher Aalternative | The Interdisciplinary Graduate School of Science and Engineering
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| NII Type |
Departmental Bulletin Paper
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| Format |
PDF
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| Text Version |
出版社版
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| OAI-PMH Set |
Faculty of Science and Engineering
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| 他の一覧 |
