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October 2016 The metric growth of the discrete Laplacian
Hisayasu KURATA, Maretsugu YAMASAKI
Hokkaido Math. J. 45(3): 399-417 (October 2016). DOI: 10.14492/hokmj/1478487617

Abstract

Networks play important roles in the theory of discrete potentials. Especially, the theory of Dirichlet spaces on networks has become one of the most important tools for the study of potentials on networks. In this paper, first we study some relations between the Dirichlet sums of a function and of its Laplacian. We introduce some conditions to investigate properties of several functional spaces related to Dirichlet potentials and to biharmonic functions. Our goal is to study the growth of the Laplacian related to biharmonic functions on an infinite network. As an application, we prove a Riesz Decomposition theorem for Dirichlet functions satisfying various conditions.

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Hisayasu KURATA. Maretsugu YAMASAKI. "The metric growth of the discrete Laplacian." Hokkaido Math. J. 45 (3) 399 - 417, October 2016. https://doi.org/10.14492/hokmj/1478487617

Information

Published: October 2016
First available in Project Euclid: 7 November 2016

zbMATH: 1353.31008
MathSciNet: MR3568635
Digital Object Identifier: 10.14492/hokmj/1478487617

Subjects:
Primary: 31C20
Secondary: 31C25

Rights: Copyright © 2016 Hokkaido University, Department of Mathematics

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Vol.45 • No. 3 • October 2016
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