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Φ-Bounded Harmonic Functions and the Classification of Harmonic Spaces

Published online by Cambridge University Press:  22 January 2016

Wellington H. Ow
Wellington H. Ow*
Affiliation:
Michigan State University
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By a harmonic space we mean a pair (X, H) where X is a locally compact, non-compact, connected, locally connected Hausdorff space ; and H is a sheaf of harmonic functions defined as follows: Suppose to each open set Ω ⊂ X there corresponds a linear space H(Ω) of finitely-continuous real-valued functions defined on Ω. Then H = {H(Ω)}Ω must satisfy the three axioms of Brelot (1) and in addition Axiom 4 of Loeb (4): 1 is H-superharmonic in X.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 48 , December 1972 , pp. 57 - 65
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1972

References

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