Function spaces of dominating mixed smoothness, Weyl and Bernstein numbers / von M.Sc. Van Kien Nguyen

Function spaces of dominating mixed smoothness were first introduced in the early sixties. Recently, there is an increasing interest in those spaces in information-based complexity and high-dimensional approximation. In this work, on the one hand, we concentrate on studying some further properties of Besov-Triebel-Lizorkin spaces of dominating mixed smoothness such as pointwise multiplication, characterization by mixed differences, and change of variable operators which are connected to numerous applications. On the other hand, we investigate the order of convergence of Weyl and Bernstein numbers of compact embeddings of tensor product Sobolev and Besov spaces into Lebesgue spaces on the unit cube. These quantities belong to the class so-called s-numbers and play an important role in the study of the complexity problems since they are lower bounds for worst-case approximation errors. Our method is based on the wavelet decomposition of Besov-Triebel-Lizorkin spaces of dominating mixed smoothness to reduce the problem to analyzing Weyl and Bernstein numbers in the level of sequence spaces.

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Person: Nguyen, Van Kien [Author]
Corporate Author: Friedrich-Schiller-Universität Jena [Degree granting institution]
Format: Book
Language(s):English
Language note:Zusammenfassungen in deutscher und englischer Sprache
Publication:Jena, 2017
Printing place:Jena
Dissertation Note:Dissertation, Friedrich-Schiller-Universität Jena, 2017
Subjects:Approximationstheorie
Type of content:Hochschulschrift
Related resources:Erscheint auch als Online-Ausgabe: Function spaces of dominating mixed smoothness, Weyl and Bernstein numbers
Physical description:xiv, 138 Seiten ; 30 cm
Basic Classification: 31.49 Analysis: Sonstiges
Further information:Inhaltsverzeichnis