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 Wavelets in function spaces on cellular domains

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Nowadays the theory and application of wavelet decompositions plays an important role not only for the study of function spaces of Lebesgue, Hardy, Sobolev, Besov, Triebel-Lizorkin type but also for its applications in signal and numerical analysis, partial differential equations and image processing. In this context it it a hard problem to construct wavelet bases for suitable function spaces on domains, e. g. the unit cube. A big step in this direction are the contributions of Hans Triebel from 2006 to 2008 where he constructed Riesz bases for classes of Besov- and Triebel-Lizorkin spaces on domains, starting with Daubechies wavelets. But there was a problem coming from the method: He had to exclude a big number of function spaces, in particular a large class of classical Sobolev spaces. The main goal of this thesis is a construction of Riesz bases of wavelet systems also for the exceptional cases using a modification of the function spaces - the so-called reinforced function spaces.

Autor: Benjamin Scharf

Fuente: https://archive.org/

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