Capacities on Harmonic Spaces with Adjoint Structure

Fumi-Yuki Maeda
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Fumi-Yuki Maeda: Hiroshima University, Department of Mathematics, Faculty of Science

A chapter in Potential Theory, 1988, pp 231-236 from Springer

Abstract: Abstract In the classical potential theory, the capacities defined in terms of Green potentials coincide with the capacity defined by Dirichlet integrals; more precisely, for a compact set K in a Greenian domain Ω in ℝd, $$Sup\{ \mu (\Omega )|G\mu \leqq 1,\,Supp\,\mu \subset K\} = \inf \{ \smallint G\mu \,d\mu |G\mu \geqq 1\,on\,K\} = \,\inf \{ D[f]\,|\,f:\,potential\,on\,\Omega \,with\,f \geqq 1\,on\,K\}$$ , where Gμ is the Green potential of μ ≧ 0 on Ω and D[f] is the Dirichlet integral of f.

Date: 1988
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DOI: 10.1007/978-1-4613-0981-9_30

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