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 ...

We present a definition of holomorphic function and an approach to the Cauchy theory that presents complex function theory as a natural outgrowth of multivariable calculus.