Abstract
We obtain criteria for harmonicity and subharmonicity of a function in a domain in R d, d≥2, in terms of special Arens–Singer and Jensen measures. We also establish a criterion for (sub-)harmonicity of a δ-subharmonic function in terms of the associated Riesz charge and special Arens–Singer and Jensen functions. To this end, we use the theorem of this article on continuation of (sub-)harmonic functions to polar sets.
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Khabibullin, B.N. Criteria for (Sub-)Harmonicity and Continuation of (Sub-)Harmonic Functions. Siberian Mathematical Journal 44, 713–728 (2003). https://doi.org/10.1023/A:1024796809786
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DOI: https://doi.org/10.1023/A:1024796809786