arXiv subjects
Publications and source records attributed to F. M. Baêta.
We consider functional ellipsoids in the sense defined by Ivanov and Naszódi and we study the problem of constructing a decomposition of the identity similar to the one given by Fritz John in his fundamental theorem.
Given a convex body $K \subseteq \mathbb R^n$ in Löwner position we study the problem of constructing a non-negative centered isotropic measure supported in the contact points, whose existence is guaranteed by John's Theorem. The method we propose requires the minimization of a convex function defined in an $\frac {n(n+3)}2$ dimensional vector space. We find a geometric interpretation of the minimizer as $\left. \frac{\partial}{\partial r}(A_r, v_r)\right|_{r=1}$, where $A_r K + v_r$ is a one-parameter family of positions of $K$ that are in some sense related to the maximal intersection position of radius $r$ defined recently by Artstein-Avidan and Katzin.