337 research outputs found
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
Hardy Wavelet Induced Isomorphism
The present thesis titled Hardy Wavelet Induced Isomorphism "consists of three chapters. The rst chapter is the introductory chapter about Hardy space, Hardy wavelets and MRA. The second and third chapters consist of denition and examples of Hardy wavelet induced isomorphisms and their xed point sets in case of two-interval Hardy wavelet sets
The C*-algebra of a vector bundle and fields of Cuntz algebras
We study the Pimsner algebra associated with the module of continuous
sections of a Hilbert bundle, and prove that it is a continuous bundle of Cuntz
algebras. We discuss the role of such Pimsner algebras w.r.t. the notion of
inner endomorphism. Furthermore, we study bundles of Cuntz algebras carrying a
global circle action, and assign to them a class in the representable KK-group
of the zero-grade bundle. We compute such class for the Pimsner algebra of a
vector bundle.Comment: 37 page
- …