KHÔI PHỤC VÀ XẤP XỈ HÀM SỐ TUẦN HOÀN BẰNG PHƯƠNG PHÁP THÍCH NGHI TRONG KHÔNG GIAN BESOV VỚI ĐỘ TRƠN HỖN HỢP

Abstract

For multivariate Besov-type classes ,
a p
U θ of functions having nonuniform mixed
smoothness a ∈ d+ , we obtain the asumptotic order of entropy numbers εn (Upa,θ, Lq )and non-linear widths
(
)
,
a , n p q
U L
θ
ρ
defined via pseudo-dimension. We obtain also the asymptotic order of optimal methods of adaptive sampling recovery by sets of a finite capacity which is measured by their cardinality or pseudo-dimension.
Keywords: Besov-type spaces, nonlinear approximation, pseudo-dimension.