Chapter 4 – Convex Geometry and Functional Analysis

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A Continuous Version of the Brascamp-Lieb Inequalities (2004, background): “Keith Ball’s version of the Brascamp–Lieb inequality (see [BrL, B2, B3] and the survey [ B1 ]) and its inverse form [Ba1, Ba2] involve a decomposition of the identity”
Subadditivity of The Entropy and its Relation to Brascamp–Lieb Type Inequalities (2007, methodology): “As explained in the introduction, we are mainly interested in the case (Mj, Mj ,ν j )= (R, B ,ν ) for all j ≤ m ,w hereν is the Lebesgue measure on R. Theorem 2.1.”
Signal Recovery From Random Measurements Via Orthogonal Matching Pursuit (2007, background): “Sidak’s Lemma [ Bal02 , Lemma 2] shows that the Gaussian measure of this intersection is no smaller than the product of the measures of the slabs.”
An arithmetic proof of John’s ellipsoid theorem (2005, methodology): “For references to other proofs, a generalization and to the numerous applications see [ 2 , 6, 8, 12].”