Gerlind Plonka
Approximation Properties of Multi--Scaling Functions: A Fourier Approach
Preprint series: Rostocker Mathematische Kolloquium, Rostock. Math. Kolloq. 49, 115-126 (1995)
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 $\f_{\nu}$ $(\nu=0, \ldots , r-1)$ which are
not necessarily compactly supported, but have a suitable decay rate.
Assuming that the function vector $\ff= (\f_{\nu})_{\nu=0}^{r-1}$ is
refinable, we sketch a new way, how to derive
necessary and sufficient conditions for the refinement mask
in Fourier domain.
Keywords: Approximation Order, Refinement Mask, Strong-Fix Conditions