Löwner’s theorem

A real function $f$ on an interval $I$ is matrix monotone if and only if it is real analytic and has (complex) analytic continuations to the upper and lower half planes such that $\mathrm{\Im }(f)>0$ in the upper half plane.

(Löwner 1934)

Title	Löwner’s theorem
Canonical name	LownersTheorem
Date of creation	2013-03-22 13:34:49
Last modified on	2013-03-22 13:34:49
Owner	mathcam (2727)
Last modified by	mathcam (2727)
Numerical id	7
Author	mathcam (2727)
Entry type	Theorem
Classification	msc 40A30