منابع مشابه
Averages of norms and quasi - norms ∗
We compute the number of summands in q-averages of norms needed to approximate an Euclidean norm. It turns out that these numbers depend on the norm involved essentially only through the maximal ratio of the norm and the Euclidean norm. Particular attention is given to the case q = ∞ (in which the average is replaced with the maxima). This is closely connected with the behavior of certain famil...
متن کاملNorms of Modes and Quasi-modes Revisited
This article is devoted to the analysis of eigenfunctions (modes) and approximate eigenfunctions (quasi-modes) of the Laplacian on a compact manifold (M, g) with completely integrable geodesic flow. We give a new proof of the main result of [TZ] that (M, g) with integrable Laplacians and with uniformly bounded eigenfunctions must be flat. The proof is based on the use of Birkhoff normal forms a...
متن کاملSelf-dual and quasi self-dual algebras
A self-dual algebra is an associative or Lie algebra A together with an A bimodule isomorphism A → A∨op, where A∨ = Homk(A, k), the dual bimodule to A (considered as an A bimodule), and A∨op is the the same underlying k module as A∨ but is an A bimodule whose left operation by an element a ∈ A is the same as the right operation by a on A∨, and similarly with left and right interchanged. This in...
متن کاملGruenhage Compacta and Strictly Convex Dual Norms
We prove that if K is a Gruenhage compact space then C (K) admits an equivalent, strictly convex dual norm. As a corollary, we show that if X is a Banach space and X∗ = span|||·|||(K), where K is a Gruenhage compact in the w∗-topology and ||| · ||| is equivalent to a coarser, w∗-lower semicontinuous norm on X∗, then X∗ admits an equivalent, strictly convex dual norm. We give a partial converse ...
متن کاملSmall Ball Estimates for Quasi-norms
This note contains two types of small ball estimates for random vectors in finite dimensional spaces equipped with a quasi-norm. In the first part, we obtain bounds for the small ball probability of random vectors under some smoothness assumptions on their density function. In the second part, we obtain Littlewood-Offord type estimates for quasi-norms. This generalizes a result which was previo...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1969
ISSN: 0002-9939
DOI: 10.2307/2037510