Annals of Mathematics, Second Series, Vol. 176, No. 3 (November, 2012), pp. 1783-1826 (44 pages) We prove generalizations of Löwner's results on matrix monotone functions to several variables. We give ...

Let $f(z_1,\ldots,z_n)$ be an entire function of the $n(\geqq 2)$ complex variables $z_1,\ldots,z_n$ holomorphic for $|z_t| \leqq r_t, t = 1,\ldots n$. We have ...