TL;DR
This paper investigates the Feller property for Laplacians on infinite graphs, providing conditions, characterizations, and comparison results that extend understanding of function preservation at infinity in graph-based operators.
Contribution
It introduces new conditions involving curvature for the Feller property on general graphs and characterizes this property in model graphs.
Findings
Conditions involving curvature-type quantities ensure the Feller property.
Characterization of the Feller property in specific model graphs.
Comparison results linking general graphs to model cases.
Abstract
The Feller property concerns the preservation of the space of functions vanishing at infinity by the semigroup generated by an operator. We study this property in the case of the Laplacian on infinite graphs with arbitrary edge weights and vertex measures. In particular, we give conditions for the Feller property involving curvature-type quantities for general graphs, characterize the property in the case of model graphs, and give some comparison results to the model case.
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