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2014 Convex and subharmonic functions on graphs
Matthew Burke, Tony Perkins
Involve 7(2): 227-237 (2014). DOI: 10.2140/involve.2014.7.227

Abstract

We explore the relationship between convex and subharmonic functions on discrete sets. Our principal concern is to determine the setting in which a convex function is necessarily subharmonic. We initially consider the primary notions of convexity on graphs and show that more structure is needed to establish the desired result. To that end, we consider a notion of convexity defined on lattice-like graphs generated by normed abelian groups. For this class of graphs, we are able to prove that all convex functions are subharmonic.

Citation

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Matthew Burke. Tony Perkins. "Convex and subharmonic functions on graphs." Involve 7 (2) 227 - 237, 2014. https://doi.org/10.2140/involve.2014.7.227

Information

Received: 1 April 2013; Revised: 21 June 2013; Accepted: 5 July 2013; Published: 2014
First available in Project Euclid: 20 December 2017

zbMATH: 1282.05059
MathSciNet: MR3133721
Digital Object Identifier: 10.2140/involve.2014.7.227

Subjects:
Primary: 26A51‎
Secondary: 31C20

Rights: Copyright © 2014 Mathematical Sciences Publishers

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Vol.7 • No. 2 • 2014
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