John's Decomposition of the Identity in the Non-Convex Case

John's Decomposition of the Identity in the Non-Convex Case We prove an extension of the classical John's Theorem, that characterises the ellipsoid of maximal volume position inside a convex body by the existence of some kind of decomposition of the identity, obtaining some results for maximal volume position of a compact and connected set inside a convex set with nonempty interior. By using those results we give some estimates for the outer volume ratio of bodies not necessarily convex. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

John's Decomposition of the Identity in the Non-Convex Case

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Publisher
Kluwer Academic Publishers
Copyright
Copyright © 2002 by Kluwer Academic Publishers
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1023/A:1012087231191
Publisher site
See Article on Publisher Site

Abstract

We prove an extension of the classical John's Theorem, that characterises the ellipsoid of maximal volume position inside a convex body by the existence of some kind of decomposition of the identity, obtaining some results for maximal volume position of a compact and connected set inside a convex set with nonempty interior. By using those results we give some estimates for the outer volume ratio of bodies not necessarily convex.

Journal

PositivitySpringer Journals

Published: Oct 12, 2004

References

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