Limits of harmonic functions on $\mathbb{Z}^{d}$

We give an example of a sequence of positive harmonic functions on \mathbb{Z}^{d} , d\geq 2 , that converges pointwise to a non-harmonic function.

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Publication Details

Journal
L’Enseignement Mathématique
Published
2026-10-14
DOI
https://doi.org/10.4171/lem/1109
Primary Topic
Geometric Analysis and Curvature Flows
Type
article
Field-Weighted Citation Impact
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article

Limits of harmonic functions on $\mathbb{Z}^{d}$

Ferdinand Jacobé de Naurois
L’Enseignement Mathématique
Geometric Analysis and Curvature Flows
article

Limits of harmonic functions on $\mathbb{Z}^{d}$

Ferdinand Jacobé de Naurois
article en

Abstract

We give an example of a sequence of positive harmonic functions on \mathbb{Z}^{d} , d\geq 2 , that converges pointwise to a non-harmonic function.

L’Enseignement Mathématique
University of Oxford (GB)
Openalex Percentile: Top 98%
Geometric Analysis and Curvature Flows
DOIOpen Access PDFOpenAlex
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