Kai Bittner
Optimal Bell Functions for Biorthogonal Local Trigonometric Bases
Preprint series: Preprints aus dem Fachbereich Mathematik, Universität Rostock

MSC:

41A25 Rate of convergence, degree of approximation

41A30 Approximation by other special function classes

42A10 Trigonometric approximation

Abstract: A general approach for biothogonal local trigonometric bases
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.
Keywords: local trigonometric bases, wavelets, biorthogonality