Helmholtz operators on infinite graphs

Varadha Raj Manivannan; Madhu Venkataraman

doi:10.1016/j.heliyon.2024.e24761

Heliyon (Jan 2024)

Helmholtz operators on infinite graphs

Varadha Raj Manivannan,
Madhu Venkataraman

Affiliations

Varadha Raj Manivannan: Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore - 632 014, Tamil Nadu, India
Madhu Venkataraman: Corresponding author.; Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore - 632 014, Tamil Nadu, India

DOI: https://doi.org/10.1016/j.heliyon.2024.e24761
Journal volume & issue: Vol. 10, no. 2
p. e24761

Abstract

Read online

The Helmholtz equation in its simplest form is Δu(a)=−k2u(a). In this note, we study a generalized discrete version of this equation on an infinite graph, by using potential-theoretic methods.

Published in Heliyon

ISSN: 2405-8440 (Online)
Publisher: Elsevier
Country of publisher: United Kingdom
LCC subjects: Science: Science (General); Social Sciences: Social sciences (General)
Website: https://www.cell.com/heliyon/home

About the journal

Abstract

Keywords