Nonstational Dual Wavelet Frames in Sobolev Spaces

Characterization of Sobolev Spaces of Arbitrary Smoothness Using Nonstationary Tight Wavelet Frames

In this paper we shall characterize Sobolev spaces of an arbitrary order of smoothness using nonstationary tight wavelet frames for L2(R). In particular, we show that a Sobolev space of an arbitrary fixed order of smoothness can be characterized in terms of the weighted `2-norm of the analysis wavelet coefficient sequences using a fixed compactly supported nonstationary tight wavelet frame in L...

Recent Developments on Dual Wavelet Frames

In this article, we discuss some recent developments on pairs of dual wavelet frames in Sobolev spaces constructed by the Oblique Extension Principle (OEP) from refinable function vectors. Our investigation sheds a new light on understanding the OEP method for constructing MRA dual wavelet frames.

Dual multiwavelet frames with symmetry from two-direction renable functions

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} ...

Flexible Gabor - wavelet atomic decompositions for L 2 - Sobolev spaces

In this paper we present a general construction of frames, which allows one to ensure that certain families of functions (atoms) obtained by a suitable combination of translation, modulation, and dilation will form Banach frames for the family of L2-Sobolev spaces on R of any order. In this construction a parameter α ∈ [0, 1) governs the dependence of the dilation factor on the frequency parame...