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 ...

Functions on Euclidean Spaces Differential Calculus in Several Variables Integral Calculus in Several Variables Change of Variables Formula, Improper Multiple Integrals Line and Surface Integrals ...

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 ...