Error estimates and reproduction of polynomials for biorthogonal local trigonometric bases

A general approach for biorthogonal local trigonometric bases in the two-ov erlapping setting was given by Chui and Shi. In this paper, we give error e stimates for the approximation with such basis functions. In particular, it is shown that for a partition of the real axis into small intervals one ob tains better approximation order if polynomials are reproduced locally. Fur thermore, smooth trigonometric bases are constructed, which reproduce const ants resp. linear functions by only one resp. a small number of basis funct ions for each interval. (C) 1999 Academic Press.