n-Widths of function spaces
نویسندگان
چکیده
منابع مشابه
Widths of embeddings in function spaces
We study the approximation, Gelfand and Kolmogorov numbers of embeddings in function spaces of Besov and Triebel-Lizorkin type. Our aim here is to provide sharp estimates in several cases left open in the literature and give a complete overview of the known results. We also add some historical remarks. AMS Classification: 41A45, 41A46, 46E35
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In this paper we derive optimal subspaces for Kolmogorov n-widths in the L2 norm with respect to sets of functions defined by kernels. This enables us to prove the existence of optimal spline subspaces of arbitrarily high degree for certain classes of functions in Sobolev spaces of importance in finite element methods. We construct these spline spaces explicitly in special cases. Math Subject C...
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Let W~ r) = {f:fecr-J[O, l ] , f (rl) abs. cont., Ilftr)IIp < oo}, and set B~) = {f: f~ ~ ' ) , I[/~r)llp ~ 1}. We find the exact Kolmogorov, Gerfand, linear, and Bernstein n-widths of B~p r) in L p for all pE(l, oo). For the Kolmogorov n-width we show that for n _> r there exists an optimal subspace of splines of degree r 1 with n r fixed simple knots depending on p,
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chapter one is devoted to a moderate discussion on preliminaries, according to our requirements. chapter two which is based on our work in (24) is devoted introducting weighted semigroups (s, w), and studying some famous function spaces on them, especially the relations between go (s, w) and other function speces are invesigated. in fact this chapter is a complement to (32). one of the main fea...
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ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 1976
ISSN: 0021-9045
DOI: 10.1016/0021-9045(76)90096-4