Hokkaido Mathematical Journal

The metric growth of the discrete Laplacian

Hisayasu KURATA and Maretsugu YAMASAKI

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

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.

Article information

Source
Hokkaido Math. J., Volume 45, Number 3 (2016), 399-417.

Dates
First available in Project Euclid: 7 November 2016

Permanent link to this document
https://projecteuclid.org/euclid.hokmj/1478487617

Digital Object Identifier
doi:10.14492/hokmj/1478487617

Mathematical Reviews number (MathSciNet)
MR3568635

Zentralblatt MATH identifier
1353.31008

Subjects
Primary: 31C20: Discrete potential theory and numerical methods
Secondary: 31C25: Dirichlet spaces

Keywords
discrete potential theory discrete Laplacian Riesz Decomposition

Citation

KURATA, Hisayasu; YAMASAKI, Maretsugu. The metric growth of the discrete Laplacian. Hokkaido Math. J. 45 (2016), no. 3, 399--417. doi:10.14492/hokmj/1478487617. https://projecteuclid.org/euclid.hokmj/1478487617


Export citation