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Zbl 1172.41306
Vyb\'iral, Jan
On dilation operators and sampling numbers.
(English)
[J] J. Funct. Spaces Appl. 6, No. 1, 17-46 (2008). ISSN 0972-6802

The author considers the dilation operators $T_k$ in the frame of Besov spaces $B_{pq}^{s}(\bbfR^d),1\leq p,q\leq\infty$. The case $s=0$ is also studied in the present paper. It is observed that new effects based on Littlewood-Paley theory appear. In the other part of the paper author apply these results to the study of so called sampling numbers.
[Vijay Gupta (New Delhi)]
MSC 2000:
*41A25 Degree of approximation, etc.
41A46 Approximation by arbitrary nonlinear expressions
46E35 Sobolev spaces and generalizations

Keywords: linear and nonlinear approximation methods; Besov spaces; dilation operators; sampling operators

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