Counting Via Entropy: New Preasymptotics for the Approximation Numbers of Sobolev Embeddings
نویسندگان
چکیده
منابع مشابه
Counting Via Entropy: New Preasymptotics for the Approximation Numbers of Sobolev Embeddings
We study the optimal linear L2-approximation by operators of finite rank (i.e., approximation numbers) for the isotropic periodic Sobolev space Hs(Td) of fractional smoothness on the d-torus. For a family of weighted norms, which penalize Fourier coefficients f̂(k) by a weight ws,p(k) = (1 + ‖k‖p), 0 < p ≤ ∞, we prove that the n-th approximation number of the embedding Id : Hs(Td) → L2(T) is cha...
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ژورنال
عنوان ژورنال: SIAM Journal on Numerical Analysis
سال: 2016
ISSN: 0036-1429,1095-7170
DOI: 10.1137/16m106580x