Gelfand numbers of embeddings of mixed Besov spaces

Let Sp1,p1tB((0,1)d) be the Besov spaces with dominating mixed smoothness on (0,1)d. In this paper we consider the problem App:Sp1,p1tB((0,1)d)→Lp2((0,1)d) and investigate the asymptotic behaviour of Gelfand numbers of this embedding. We shall give the correct order of convergence of Gelfand numbers...

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Bibliographic Details
Published in:Journal of Complexity 2017-08, Vol.41, p.35-57
Main Author: Nguyen, Van Kien
Format: Article
Language:English
Subjects:
Approximation numbers
Besov spaces
Compact embeddings
Dominating mixed smoothness
Gelfand numbers
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Summary:Let Sp1,p1tB((0,1)d) be the Besov spaces with dominating mixed smoothness on (0,1)d. In this paper we consider the problem App:Sp1,p1tB((0,1)d)→Lp2((0,1)d) and investigate the asymptotic behaviour of Gelfand numbers of this embedding. We shall give the correct order of convergence of Gelfand numbers in almost all cases. In addition we shall compare these results with the known behaviour of approximation numbers.
ISSN:0885-064X
1090-2708
DOI:10.1016/j.jco.2016.11.004