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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
Journal Title
Memoirs of the Graduate School of Science and Engineering, Shimane University. Series B, Mathematics
Volume
55
Start Page
1
End Page
25
ISSN
1342-7121
Published Date
2022
DOI(SelfDOI)
Publisher
総合理工学部
Publisher Aalternative
The Interdisciplinary Graduate School of Science and Engineering
NII Type
Departmental Bulletin Paper
Format
PDF
Text Version
出版社版
OAI-PMH Set
Faculty of Science and Engineering
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