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Maximum Principles in the Potential Theory

Published online by Cambridge University Press:  22 January 2016

Masanori Kishi
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Ninomiya, in his thesis [13] on the potential theory with respect to a positive symmetric continuous kernel G on a locally compact Hausdorff space Ω, proves that G satisfies the balayage (resp. equilibrium) principle if and only if G satisfies the domination (resp. maximum) principle. He starts from the Gauss-Ninomiya variation and shows that for any given compact set K in Ω and any positive upper semi-continuous function u on K, there exists a positive measure μ on K such that its potential Gμ is ≥ u on the support of μ and Gμ≥u on K almost everywhere with respect to any positive measure with finite energy.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 23 , December 1963 , pp. 165 - 187
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1963

References

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