Gerlind Plonka, Vasily Strela
From Wavelets to Multiwavelets
Preprint series: Preprints aus dem Fachbereich Mathematik, Universität Rostock
41-02 Research exposition (monographs, survey articles)
41-06 Proceedings, conferences, collections, etc.
41A30 Approximation by other special function classes
42A85 Convolution, factorization
42C15 Series of general orthogonal functions, generalized Fourier expansions, nonorthogonal expansions
Abstract: This paper gives an overview of recent achievements of the
multiwavelet theory. The construction of multiwavelets is based on a
multiresolution analysis with higher multiplicity generated by a scaling vector.

The basic properties of scaling vectors such as L^2-stability, approximation
order and regularity are studied. Most of the proofs are sketched.
Keywords: multiwavelets, L^2-stability, approximation order, regularity, scaling vectors