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...

In this article we obtain families of frames for the space Bω of functions with band in [−ø, ø] by using the theory of shift-invariant spaces. Our results are based on the Gramian analysis of A. Ron and Z. Shen and a variant, due to Bownik, of their characterization of families of functions whose shifts form frames or Riesz bases. We give necessary and sufficient conditions for the translates o...

Let φ be a compactly supported refinable function in L2(R) such that the shifts of φ are stable and φ̂(2ξ) = â(ξ)φ̂(ξ) for a 2π-periodic trigonometric polynomial â. A wavelet function ψ can be derived from φ by ψ̂(2ξ) := e−iξ â(ξ + π)φ̂(ξ). If φ is an orthogonal refinable function, then it is well known that ψ generates an orthonormal wavelet basis in L2(R). Recently, it has been shown in the liter...

In this work, a sort of binary wavelet packages with multi-scale are introduced, which are generalizations of multivariant wavelet packages. Finitely Supported wavelet bases for Sobolev spaces is researched. Steming from a pair of finitely supported refinale functions with multi-scaled dilation factor in space 2 2 ( ) L R satsfying a very mild condition, we provide a novel method for designing ...

for all f ∈ H . The constant A (respectively, B) is a lower (resp. upper) frame bound for the frame. One of the most important frames for applications, especially signal processing, are the Weyl-Heisenberg frames. For g ∈ L(R) we define the translation parameter a > 0 and the modulation parameter b > 0 by: Embg(t) = e , Tnag(t) = g(t− na). For g ∈ L(R) and a, b > 0, we say for short that (g, a,...

For Gabor sets, (g; a, b), it is known that (g; a, b) is a frame if and only if (g; 1/b, 1/a) is a Riesz basis for its span. In particular, for every g there is a0 such that for every a < a0, there is a bm = bm(a) > 0 so that for every b < bm, (g; a, b) is a frame, and (g; 1/b, 1/a) is a Riesz basis sequence. In this talk we shall consider a similar problem for wavelet sets (Ψ; a, b). The main ...

The concept of an MV-algebra was introduced by Chang [4] as an algebraic basis for many-valued logic. It turned out that MV-algebras are a subclass of a more general class of effect algebras [7, 6]. Namely, MV-algebras are in one-to-one correspondence with lattice ordered effect algebras satisfying the Riesz decomposition property [2], the latter are called MV-effect algebras. In the study of c...