Approximation of Sobolev-type Classes with Quasi-seminorms
نویسندگان
چکیده
Since the Sobolev set W r p , 0 < p < 1, in general is not contained in Lq , 0 < q ≤ ∞. We limit ourselves to the set W r p ∩ L∞, 0 < p < 1. We prove that the Kolmogorov n-width of the latter set in Lq , 0 < q < 1 is asymptotically 1, that is, the set cannot be approximated by n-dimensional linear manifolds in the Lq-norm. We then describe a related set, the width of which is asymptotically n−r.
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