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Convex and
subharmonic functions on graphs
Matthew J. Burke and Tony L. Perkins
Vol. 7 (2014), No. 2, 227–237
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Abstract |
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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. |
Keywords
convex, subharmonic, discrete, graphs
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Mathematical Subject Classification 2010
Primary: 26A51
Secondary: 31C20
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Milestones
Received: 1 April 2013
Revised: 21 June 2013
Accepted: 5 July 2013
Published: 16 November 2013
Communicated by Ronald Gould
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Authors |
| Matthew J. Burke | |
| Spring Hill College 4000 Dauphin Street Mobile, AL 36608-1791 United States |
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| Tony L. Perkins | |
| Department of Mathematics Spring Hill College 4000 Dauphin Street Mobile, AL 36608-1791 United States |
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