On the growth of subharmonic functions in space
Let \(D_ m\) be the set of functions \(u=u_ 1-u_ 2\) such that \(u(0)=0\) and the Nevanlinna characteristic \(T(r)\) of \(u\) converges to infinity as \(r\to\infty\), where \(u_ 1\) and \(u_ 2\) are subharmonic functions in \(\mathbb{R}^ m\). The author extends the Tauberian Theorem 1 of \textit{A. Edrei} and \textit{W. H. J. Fuchs} [Comment. Math. Helv. 33, 258-295 (1959; Zbl 0090.288)], which was proved for meromorphic functions, to functions \(u\) in \(D_ m\).
scientific article; zbMATH DE number 60450
scientific article