Gerlind Plonka
Approximation properties of Multi-Scaling functions: A Fourier Approach
Preprint series: Preprints aus dem Fachbereich Mathematik, Universität Rostock
41A25 Rate of convergence, degree of approximation
41A30 Approximation by other special function classes
Abstract: In this paper, we consider approximation properties of a
finite set of functions $\phi_\nu(\nu=0,\ldots ,r-1)$
which are not necessarily compactly supported, but have
a suitable decay rate. Assuming that the function vector
=(\phi_\nu)^{r-1}_{\nu =0}$}$ is refinementable, we sketch
a new way, how to derive necessary and sufficient conditions
for the refinement mask in Fourier domain.
Keywords: Refinable function vectors, Refinement mask, Fourier transform