**MSC:**- 41A25 Rate of convergence, degree of approximation
- 41A30 Approximation by other special function classes
- 42A10 Trigonometric approximation

in the two-overlapping setting was given by Chui and Shi.

In this paper, we give error estimates for the approximation

with such basis functions. In particular, it is shown that

for a partition of the real axis into small intervals one

obtains better approximation order if polynomials are

reproduced locally. Furthermore, smooth trigonometric

bases are constructed, which reprodcure constants resp.

linear functions by only one resp. a small number of basis

functions for each interval.