Behaviour of the approximation numbers of a Sobolev embedding in the one-dimensional case

Edmunds, David and Lang, J. 2004. Behaviour of the approximation numbers of a Sobolev embedding in the one-dimensional case. Journal of Functional Analysis 206 (1) , pp. 149-166. 10.1016/S0022-1236(03)00109-5

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Abstract

We consider the Sobolev embeddings E1 : W01,p(a,b)→Lp(a,b) and E2 : L1,p(a,b)/{1}→Lp(a,b)/{1}, with −∞<a<b<∞ and 1<p<∞. We show that the approximation numbers an(Ei) of Ei have the property that where cp is a constant dependent only on p. Moreover, we show the precise value of an(E1) and we study the unbounded Sobolev embedding E3 : L1,p(a,b)→Lp(a,b) and determine precisely how closely it may be approximated by n-dimensional linear maps. Mathematical subject codes: 47G10; 47B10

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Uncontrolled Keywords:	Approximation numbers ; Sobolev embedding ; Hardy-type operators ; Integral operators
ISSN:	1096-0783
Last Modified:	18 Oct 2017 09:29
URI:	https://orca.cardiff.ac.uk/id/eprint/1736

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