Relative widths of smooth functions determined by fractional order derivatives
For two Subsets W and V of a normed space X. The relative Kolmogorov n-width of W relative to V in X is defined by K-n(W, V)(X) := inf(Ln) sup(f is an element of W) inf(g is an element of V boolean AND Ln) parallel to f - g parallel to(X), where the infimum is taken over all n-dimensional subspaces L-n of X. For alpha is an element of R+, define W-p(alpha) (1   1-1/q and the case p=1, 2   3-1/q, we obtain their weak asymptotic results. In addition, we also obtain the weak asymptotic result of W-p(alpha) relative to W-p(alpha) in the space L-p(T) for 0 < alpha <= 2. (C) 2007 Elsevier Inc. All rights reserved.
relative width width fractional order derivatives