Construction of multivariate compactly supported prewavelets in L2 space and pre-Riesz bases in Sobolev spaces

Compactly supported wavelet bases for Sobolev spaces

In this paper we investigate compactly supported wavelet bases for Sobolev spaces. Starting with a pair of compactly supported refinable functions φ and φ̃ in L2(R) satisfying a very mild condition, we provide a general principle for constructing a wavelet ψ such that the wavelets ψjk := 2j/2ψ(2j · − k) (j, k ∈ Z) form a Riesz basis for L2(R). If, in addition, φ lies in the Sobolev space H(R), t...

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

Biorthogonal Spline-Wavelets on the Interval | Stability and Moment Conditions

This paper is concerned with the construction of biorthogonal multiresolution analyses on [0; 1] such that the corresponding wavelets realize any desired order of moment conditions throughout the interval. Our starting point is the family of biorthogonal pairs consisting of cardinal B-splines and compactly supported dual generators on IR developed by Cohen, Daubechies and Feauveau. In contrast ...

Dual Wavelet Frames and Riesz Bases in Sobolev Spaces

This paper generalizes the mixed extension principle in L2(R) of [50] to a pair of dual Sobolev spaces H(R) and H−s(Rd). In terms of masks for φ, ψ, . . . , ψ ∈ H(R) and φ̃, ψ̃, . . . , ψ̃ ∈ H−s(Rd), simple sufficient conditions are given to ensure that (X(φ;ψ, . . . , ψ), X−s(φ̃; ψ̃, . . . , ψ̃)) forms a pair of dual wavelet frames in (Hs(Rd),H−s(Rd)), where X(φ;ψ, . . . , ψ) := {φ(· − k) : k ∈ Zd} ...

Linear Independence and Stability of Piecewise Linear Prewavelets on Arbitrary Triangulations

In several areas of computational mathematics, wavelet-based algorithms are becoming popular for modelling and analyzing data, providing efficient means for hierarchical data decomposition, reconstruction, editing and compression. Such algorithms are typically based on the decomposition of function spaces into mutually orthogonal wavelet spaces, each of which is endowed with a basis. The basis ...