Abstract
We introduce the notion of Lowner (ellipsoid) function for a log-concave function and show that it is an extension of the Lowner ellipsoid for convex bodies. We investigate its duality relation to the recently defined John (ellipsoid) function (Alonso-Gutierrez et al. in J Geom Anal 28:1182–1201, 2018). For convex bodies, John and Lowner ellipsoids are dual to each other. Interestingly, this need not be the case for the John function and the Lowner function.
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