Estimation of dimension functions of band-limited wavelets

Estimation of Dimension Functions of Band-limited Wavelets

The dimension function Dψ of a band-limited wavelet ψ is bounded by n if supp ψ̂ ⊆ [− 2 n+2

Band-limited Refinable Functions for Wavelets and Framelets

Extending band-limited constructions of orthonormal refinable functions, a special class of periodic functions is used to generate a family of band-limited refinable functions. Characterizations of Riesz bases and frames formed by integer shifts of these refinable functions are obtained. Such families of refinable functions are employed to construct band-limited biorthogonal wavelet bases and b...

A Characterization of Dimension Functions of Wavelets

Band-Limited Wavelets with Subexponential Decay

It is well known that the compactly supported wavelets cannot belong to the class C∞(R) ∩ L(R). This is also true for wavelets with exponential decay. We show that one can construct wavelets in the class C∞(R)∩L2(R) that are “almost” of exponential decay and, moreover, they are band-limited. We do this by showing that we can adapt the construction of the Lemarié-Meyer wavelets [LM] that is foun...

About Band Limited up to Congruences Wavelets

If ψ is a BLc wavelet, a Chui-Shi family of redundant tight frames {Ψ(k); k ∈ Z} can be built. Its redundancy is studied through the subspaces of coefficients in l2(Z2). It will be proved that these subspaces converge to zero when ψ is a uniformly continuous wavelet. Also a Whittaker-ShannonKotel’nikov type sampling theorem will be given for discrete vector functions associated to Ψ(k). Even mo...