Tensor products of Sobolev-Besov spaces and applications to approximation from the hyperbolic cross

Authors:
Winfried Sickel;Tino Ullrich
Affiliations:
Friedrich Schiller University Jena, Mathematical Institute, Ernst-Abbe-Platz 3, D-07740, Germany;Hausdorff Centre for Mathematics, Endenicher Allee 60, D-53115 Bonn, Germany
Venue:
Journal of Approximation Theory
Year:
2009

Citing 2
Cited 4

Ten lectures on wavelets

Ten lectures on wavelets
Spaces of functions of mixed smoothness and approximation from hyperbolic crosses

Journal of Approximation Theory

The randomized complexity of indefinite integration

Journal of Complexity
Adaptive Wavelet Schemes for Parabolic Problems: Sparse Matrices and Numerical Results

SIAM Journal on Numerical Analysis
Adaptive Wavelet Methods on Unbounded Domains

Journal of Scientific Computing
Multivariate approximation by translates of the Korobov function on Smolyak grids

Journal of Complexity

Quantified Score

Hi-index	0.00

Visualization

Abstract

Besov as well as Sobolev spaces of dominating mixed smoothness are shown to be tensor products of Besov and Sobolev spaces defined on R. Using this we derive several useful characterizations from the one-dimensional case to the d-dimensional situation. Finally, consequences for hyperbolic cross approximations, in particular for tensor product splines, are discussed.