Equicontinuity of harmonic functions and compactness of potential kernels
Wolfhard Hansen
TL;DR
This paper proves equicontinuity of bounded harmonic functions within balayage spaces and uses this to establish criteria for the compactness of potential kernels, advancing understanding in potential theory and harmonic analysis.
Contribution
It introduces new criteria for the compactness of potential kernels based on equicontinuity properties of harmonic functions in balayage spaces.
Findings
Bounded harmonic functions are equicontinuous in balayage spaces.
Criteria for the compactness of potential kernels are established.
Application of equicontinuity results to potential kernel analysis.
Abstract
Within the framework of balayage spaces (the analytical equivalent of nice Hunt processes), we prove equicontinuity of bounded families of harmonic functions and apply it to obtain criteria for compactness of potential kernels.
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Taxonomy
TopicsNumerical methods in inverse problems · Differential Equations and Boundary Problems · Analytic and geometric function theory