Compactly supported wavelets and representations of the Cuntz relations , II

Construction of Compactly Supported Nonseparable Orthogonal Wavelets of L^2(R^n)

ar X iv : m at h / 99 12 12 9 v 1 [ m at h . FA ] 1 5 D ec 1 99 9 COMPACTLY SUPPORTED WAVELETS

We study the harmonic analysis of the quadrature mirror filters coming from multiresolution wavelet analysis of compactly supported wavelets. It is known that those of these wavelets that come from third order polyno-mials are parametrized by the circle, and we compute that the corresponding filters generate irreducible mutually disjoint representations of of the Cuntz algebra O 2 except at two...

Construction of a class of trivariate nonseparable compactly supported wavelets with special dilation matrix

We present a method for  the construction of compactlysupported $left (begin{array}{lll}1 & 0 & -1\1 & 1 & 0 \1 &  0 & 1\end{array}right )$-wavelets  under a mild condition. Wavelets inherit thesymmetry of the corresponding scaling function and satisfies thevanishing moment condition originating in the symbols of the scalingfunction. As an application, an  example is  provided.

Certain representations of the Cuntz relations, and a question on wavelets decompositions

We compute the Coifman-Meyer-Wickerhauser measure μ for certain families of quadrature mirror filters (QMFs), and we establish that for a subclass of QMFs, μ contains a fractal scale.

2 00 2 Wavelet Representations and Fock Space on Positive Matrices

We show that every biorthogonal wavelet determines a representation by operators on Hilbert space satisfying simple identities, which captures the established relationship between orthogonal wavelets and Cuntz-algebra representations in that special case. Each of these representations is shown to have tractable finite-dimensional co-invariant doubly-cyclic subspaces. Further, motivated by these...