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The Loewner function of a log-concave function

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 نشر من قبل Elisabeth Werner M
 تاريخ النشر 2019
  مجال البحث
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We introduce the notion of Loewner (ellipsoid) function for a log concave function and show that it is an extension of the Loewner ellipsoid for convex bodies. We investigate its duality relation to the recently defined John (ellipsoid) function by Alonso-Gutierrez, Merino, Jimenez and Villa. For convex bodies, John and Loewner ellipsoids are dual to each other. Interestingly, this need not be the case for the John function and the Loewner function.



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