Abstract
We give a complete characterization of 2π-periodic matrix weights W for which the vector-valued trigonometric system forms a Schauder basis for the matrix weighted space Lp(T;W). Then trigonometric quasi-greedy bases for Lp(T;W) are considered. Quasi-greedy bases are systems for which the simple thresholding approximation algorithm converges in norm. It is proved that such a trigonometric basis can be quasi-greedy only for p=2, and whenever the system forms a quasi-greedy basis, the basis must actually be a Riesz basis.
Original language | English |
---|---|
Journal | Journal of Mathematical Analysis and Applications |
Volume | 371 |
Issue number | 2 |
Pages (from-to) | 784-792 |
Number of pages | 9 |
ISSN | 0022-247X |
DOIs | |
Publication status | Published - 2010 |