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 ...

The operator convex functions of several variables are characterized in terms of a non-commutative generalization of Jensen's inequality, extending previous results of F. Hansen and G.K. Pedersen for ...

Bergman theory forms a cornerstone of complex analysis in several variables by providing a framework in which holomorphic functions may be studied through intrinsic reproducing kernel methods.