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• W2006460982 abstract "In this article we prove that for any orthonormal system $(varphi_j){j=1}^n subset L_2$ that is bounded in $L{infty}$, and any $1 < k < n$, there exists a subset $I$ of cardinality greater than $n-k$ such that on $mathrm{span}{varphi_i}_{i in I}$, the $L_1$ norm and the $L_2$ norm are equivalent up to a factor $mu (log mu)^{5/2}$, where $mu = sqrt{n/k} sqrt{log k}$. The proof is based on a new estimate of the supremum of an empirical process on the unit ball of a Banach space with a good modulus of convexity, via the use of majorizing measures." @default.
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• W2006460982 date "2008-01-01" @default.
• W2006460982 modified "2023-10-12" @default.
• W2006460982 title "Majorizing measures and proportional subsets of bounded orthonormal systems" @default.
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• W2006460982 doi "https://doi.org/10.4171/rmi/567" @default.
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