Hokkaido Mathematical Journal

AL-QURASHI M., ANANDAM V.,

Polysuperharmonic functions on a harmonic space.

Hokkaido Mathematical Journal, 34 (2005) pp.315-330

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Abstract

In the context of the axiomatic potential theory, we introduce the notions of polyharmonic functions and polypotentials on a Brelot harmonic space $\Omega$. For these functions,we prove some results analogous to the Riesz decomposition, balayage, domination principle, etc., which are usually associated with harmonic and superharmonic functions on $\Omega$. We also consider the polyharmonic classifications of the harmonic spaces.

MSC(Primary)31D05
MSC(Secondary)31B30
Uncontrolled Keywordsm-harmonic functions, m-potential domains