On Maximal Relative Projection Constants
نویسنده
چکیده
This article focuses on the maximum of relative projection constants over all m-dimensional subspaces of the N -dimensional coordinate space equipped with the max-norm. This quantity, called maximal relative projection constant, is studied in parallel with a lower bound, dubbed quasimaximal relative projection constant. Exploiting elegant expressions for these quantities, we show how they can be computed when N is small, before concentrating on reversing the Kadec–Snobar inequality when N does not tend to infinity. Precisely, we first prove that the (quasi)maximal relative projection constant can be lower-bounded by c √ m, with c arbitrarily close to one, when N is superlinear in m. The main ingredient is a connection with equiangular tight frames. We then prove that the lower bound c √ m holds with c < 1 when N is linear in m. The main ingredient is the semicircle law.
منابع مشابه
Approximation of Maximal Cheeger Sets by Projection
This article deals with the numerical computation of the Cheeger constant and the approximation of the maximal Cheeger set of a given subset of R. This problem is motivated by landslide modelling as well as by the continuous maximal flow problem. Using the fact that the maximal Cheeger set can be approximated by solving a rather simple projection problem, we propose a numerical strategy to comp...
متن کاملAsymptotic behaviour of the simple random walk on the 2 - dimensional comb ∗
We analyze the differences between the horizontal and the vertical component of the simple random walk on the 2-dimensional comb. In particular we evaluate by combinatorial methods the asymptotic behaviour of the expected value of the distance from the origin, the maximal deviation and the maximal span in n steps, proving that for all these quantities the order is n for the horizontal projectio...
متن کاملOn the Relative Schoenflies Theorem
We prove generalizations of the relative Schoennies extension theorem for topo-logical, quasiconformal, or bi-Lipschitz embeddings due to Gauld and VV aiss all a, and show that maximal dilatations and bi-Lipschitz constants of the extensions can be controlled.
متن کاملM ay 2 00 6 Asymptotic behaviour of the simple random walk on the 2 - dimensional comb ∗ Daniela Bertacchi Università di Milano - Bicocca
We analyze the differences between the horizontal and the vertical component of the simple random walk on the 2-dimensional comb. In particular we evaluate by combinatorial methods the asymptotic behaviour of the expected value of the distance from the origin, the maximal deviation and the maximal span in n steps, proving that for all these quantities the order is n for the horizontal projectio...
متن کامل