Related papers: Wavelet sets for crystallographic groups
Wavelet sets that are finite unions of convex sets are constructed in $\mathbb R^n$, $n\geq 2$, for dilation by any expansive matrix that has a power equal to a scalar times the identity and also has all singular values greater than $\sqrt…
Most of the examples of wavelet sets are for dilation sets which are groups. We find a necessary and sufficient condition under which subspace wavelet sets exist for dilation sets of the form $A B$, which are not necessarily groups. We…
Wavelet and frames have become a widely used tool in mathematics, physics, and applied science during the last decade. This article gives an overview over some well known results about the continuous and discrete wavelet transforms and…
For Vilenkin group only the existence of multiwavelets associated with multiresolution analysis (MRA) is known. In this paper, we have shown that by using wavelet sets we can also construct single wavelet in case of Vilenkin group which are…
A traditional wavelet is a special case of a vector in a separable Hilbert space that generates a basis under the action of a system of unitary operators defined in terms of translation and dilation operations. A Coxeter/fractal-surface…
We consider the problem of characterizing the Sobolev wavefront set of a tempered distribution $u\in\mathcal{S}'(\mathbb{R}^{d})$ in terms of its continuous wavelet transform, with the latter being defined with respect to a suitably chosen…
We construct a Continuous Wavelet Transform (CWT) on the torus $\mathbb T^2$ following a group-theoretical approach based on the conformal group $SO(2,2)$. The Euclidean limit reproduces wavelets on the plane $\mathbb R^2$ with two…
W. C. Lang determined wavelets on Cantor dyadic group by using Multiresolution analysis method. In this paper we have given characterization of wavelet sets on Cantor dyadic group providing another method for the construction of wavelets.…
This review paper is intended to give a useful guide for those who want to apply discrete wavelets in their practice. The notion of wavelets and their use in practical computing and various applications are briefly described, but rigorous…
The class of generalized shearlet dilation groups has recently been developed to allow the unified treatment of various shearlet groups and associated shearlet transforms that had previously been studied on a case-by-case basis. We consider…
We proved that for any matrix dilation and for any positive integer $n$, there exists a compactly supported tight wavelet frame with approximation order $n$. Explicit methods for construction of dual and tight wavelet frames with a given…
We consider a class of semidirect products $G = \mathbb{R}^n \rtimes H$, with $H$ a suitably chosen abelian matrix group. The choice of $H$ ensures that there is a wavelet inversion formula, and we are looking for criteria to decide under…
The notion of wavelets is defined. It is briefly described {\it what} are wavelets, {\it how} to use them, {\it when} we do need them, {\it why} they are preferred and {\it where} they have been applied. Then one proceeds to the…
We consider the coorbit theory associated to general continuous wavelet transforms arising from a square-integrable, irreducible quasi-regular representation of a semidirect product group $G = \mathbb{R}^d \rtimes H$. The existence of…
The group $G_2$ of invertible affine transformations of $\mathbb{R}^2$ has, up to equivalence, one square--integrable representation. Two new realizations of this representation are presented and novel continuous wavelet transforms, acting…
We present a unified group-theoretical derivation of the Continuous Wavelet Transform (CWT) on the circle $\mathbb S^1$ and the real line $\mathbb{R}$, following the general formalism of Coherent States (CS) associated to unitary square…
Wavelet systems on the generalized Vilenkin groups are considered. An algorithmic method for the construction of orthogonal wavelet bases is presented. These bases consist of compactly supported test functions (i.e. functions whose Fourier…
Wavelets, known to be useful in non-linear multi-scale processes and in multi-resolution analysis, are shown to have a q-deformed algebraic structure. The translation and dilation operators of the theory associate with any scaling equation…
Let G be a locally compact abelian group with compact open subgroup H. The best known example of such a group is G=Q_p, the field of p-adic rational numbers (as a group under addition), which has compact open subgroup H=Z_p, the ring of…
Coorbit spaces provide a rigorous framework for the assessment of the approximation theoretic properties of generalized wavelet systems. It is therefore useful to understand when two different wavelet systems give rise to the same scales of…