Localization of frames. II
In his paper [``Localization of frames, Banach frames, and the invertibility of the frame operator'', J. Fourier Anal. Appl. 10, No. 2, 105--132 (2004; Zbl 1055.42018)], \textit{K. Gröchenig} introduced the concept of localization of frames. One of the main features of this concept is that it leads to ``automatic expansion'' of the frame expansion in a Hilbert space to an expansion in a large class of associated Banach spaces. In the present paper, this theory is extended to certain quasi-Banach spaces (Besov spaces). This plays a role, e.g., in nonlinear approximation theory. It is proved that for localized frames, the iterative frame algorithm converges in the norm of the associated Banach spaces.
scientific article; zbMATH DE number 2081609
scientific article