Entropy number and non-linear approximations on multivariate Besov space by manifolds of finite pseudo-dimension

摘要

We determine the asymptotic order of entropy number and optimal non - linear approximations of anisotropic periodic Besov class of Brpθ(Td) (1≤p≤∞, 1≤θ≤∞ ) by manifolds of finite pseudo-dimension in the metric Lq (Td), 1≤ q≤∞, where Td is the d-dimensional torus.