Abstract:
We obtain criteria for harmonicity and subharmonicity of a function in a domain in $\mathbb{R}^d$, $d\geqslant2$, in terms of special Arens–Singer and Jensen measures. We also establish a criterion for (sub-)harmonicity of a $\delta$-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.
Citation:
B. N. Khabibullin, “Criteria for (sub-)harmonicity and continuation of (sub-)harmonic functions”, Sibirsk. Mat. Zh., 44:4 (2003), 905–925; Siberian Math. J., 44:4 (2003), 713–728