Characterizing matrix monotonicity of fixed order on general sets

Abstract

We give new characterizations for matrix monotonicity and convexity of fixed order which connects previous characterizations by Loewner, Dobsch, Donoghue, Kraus and Bendat--Sherman. The ideas introduced are then used to characterize matrix monotone functions of arbitrary order on general subsets of the real line.

16 pages, no figures

References in corpus (2)

• Divided Differences
• Differential analysis of matrix convex functions