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Mathematics > Classical Analysis and ODEs

arXiv:2202.01996 (math)
[Submitted on 4 Feb 2022]

Title:On the theory of capacities on locally compact spaces and its interaction with the theory of balayage

Authors:Natalia Zorii
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Abstract:The paper deals with the theory of inner (outer) capacities on locally compact spaces with respect to general function kernels, the main emphasis being placed on the establishment of alternative characterizations of inner (outer) capacities and inner (outer) capacitary measures for arbitrary sets. The analysis is substantially based on the close interaction between the theory of capacities and that of balayage. As a by-product, we provide a rigorous justification of Fuglede's theories of inner and outer capacitary measures and capacitability (Acta Math., 1960). The results obtained are largely new even for the logarithmic, Newtonian, Green, $\alpha$-Riesz, and $\alpha$-Green kernels.
Comments: 31 pages
Subjects: Classical Analysis and ODEs (math.CA); Complex Variables (math.CV)
MSC classes: 31C15
Cite as: arXiv:2202.01996 [math.CA]
  (or arXiv:2202.01996v1 [math.CA] for this version)
  https://doi.org/10.48550/arXiv.2202.01996

Submission history

From: Natalia Zorii [view email]
[v1] Fri, 4 Feb 2022 06:56:02 UTC (31 KB)
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