For two subsets W and V of a Banach space X, let Kn(W,V,X) denote the relative Kolmogorov n-width of W relative to V defined by
Kn(W,V,X):= infLn supf∈W inf g∈ V∩ Ln || f-g||X,
where the infimum is taken over all n-dimensional linear subspaces Ln of X. Let W2(△r) denote the class of 2π-periodic functions f with d-variables satisfying
∫[-π,π]d |△r f(x)|2,dx≤ 1,
while △r is the r-iterate of Laplace operator △. This article discusses the relative Kolmogorov n-width of W2(△r)$ relative to W2(△r) in Lq([-π,π]d),(1≤ q≤∞), and obtain its weak asymptotic result.
