Generalized interpolating refinable function vectors
Compactly supported interpolating \(d\)-refinable function vectors with any dilation factor \(d>1\) are considered. Motivated by wavelet applications, it is desirable to have compactly supported refinable functions that are both interpolating and orthogonal. But it is impossible to have a compactly supported scalar 2-refinable function such that it is both interpolating and orthogonal.Therefore it is natural to consider \(d\)-refinable function vectors. The authors characterize both interpolating \(d\)-refinable function vectors and orthogonal interpolating \(d\)-refinable function vectors in terms of their masks and study their approximation properties. A family of interpolatory masks for compactly supported interpolating \(d\)-refinable function vectors with increasing orders of sum rules is presented. Several examples of compactly supported (orthogonal) interpolating refinable function vectors and biorthogonal multiwavelets derived from such interpolating function vectors are given.
interpolating refinable function vectors
compactly supported refinable function vectors
orthogonal interpolating refinable function vectors
scientific article; zbMATH DE number 5549324