Functional Löwner Ellipsoids
نویسندگان
چکیده
We extend the notion of minimal volume ellipsoid containing a convex body in $$\mathbb {R}^{d}$$ to setting logarithmically concave functions. consider vast class functions whose superlevel sets are concentric ellipsoids. For fixed function from this class, we set all its “affine” positions. any log-concave f on {R}^{d},$$ belonging positions, and find one with integral under condition that it is pointwise greater than or equal f. study properties existence uniqueness solution problem. $$s \in [0,+\infty ),$$ construction dual recently defined John s-function (Ivanov Naszódi Functional arXiv preprint: arXiv:2006.09934, 2020). prove such determines unique call Löwner s-functions as s tends zero infinity. Finally, extending outer ratio, define ratio give an asymptotically tight bound it.
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ژورنال
عنوان ژورنال: Journal of Geometric Analysis
سال: 2021
ISSN: ['1559-002X', '1050-6926']
DOI: https://doi.org/10.1007/s12220-021-00691-4