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A Decomposition Theorem for Positive Superharmonic Functions

Published online by Cambridge University Press:  20 November 2018

Sirkka-Liisa Eriksson-Bique
Sirkka-Liisa Eriksson-Bique*
Affiliation:
Department of Mathematics University of Joensuu SF-80101 Joensuu, Finland
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Abstract

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Let X be a harmonic space in the sense of C. Constantinescu and A. Cornea. We show that, for any subset E of X, a positive superharmonic function u on X has a representation u = p + h, where p is the greatest specific minorant of u satisfying . This result is a generalization of a theorem of M. Brelot. We also state some characterizations of extremal superharmonic functions.

Keywords

31D0506A10
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 33 , Issue 3 , 01 September 1990 , pp. 286 - 296
Copyright
Copyright © Canadian Mathematical Society 1990

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