Separately Subharmonic and Harmonic Functions are Subharmonic

2009/05/06 by Kalantar, Mansour
#31B05 #54C30 #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.0905.0712

Abstract

We will prove that a function u(x,y) defined on a domain of RpxRq that is subharmonic in one variable and harmonic in the other is (jointly) subharmonic. This solves a long-standing open problem.

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