823 research outputs found
Weyl Numbers of Embeddings of Tensor Product Besov Spaces
In this paper we investigate the asymptotic behaviour of Weyl numbers of
embeddings of tensor product Besov spaces into Lebesgue spaces. These results
will be compared with the known behaviour of entropy numbers.Comment: 54 pages, 2 figure
Optimal Approximation of Elliptic Problems by Linear and Nonlinear Mappings III: Frames
We study the optimal approximation of the solution of an operator equation by
certain n-term approximations with respect to specific classes of frames. We
study worst case errors and the optimal order of convergence and define
suitable nonlinear frame widths.
The main advantage of frames compared to Riesz basis, which were studied in
our earlier papers, is the fact that we can now handle arbitrary bounded
Lipschitz domains--also for the upper bounds.
Key words: elliptic operator equation, worst case error, frames, nonlinear
approximation, best n-term approximation, manifold width, Besov spaces on
Lipschitz domainsComment: J. Complexity, to appear. Final version, minor mistakes correcte
Optimal Approximation of Elliptic Problems by Linear and Nonlinear Mappings I
We study the optimal approximation of the solution of an operator equation
Au=f by linear and nonlinear mappings
Interpolation of Morrey-Campanato and Related Smoothness Spaces
In this article, the authors study the interpolation of Morrey-Campanato
spaces and some smoothness spaces based on Morrey spaces, e.\,g., Besov-type
and Triebel-Lizorkin-type spaces. Various interpolation methods, including the
complex method, the -method and the Peetre-Gagliardo method, are studied
in such a framework. Special emphasize is given to the quasi-Banach case and to
the interpolation property.Comment: Sci. China Math. (2015
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