The problem of Taylor's series is therefore to deduce from a knowledge of the coefficients the behaviour of the function. The Taylor Series: an Introduction to the Theory of Functions of a Complex ...

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 ...