Related papers: Continuous Wavelet Frames on the Sphere: The Group…
We consider the conformal group of the unit sphere $S^{n-1},$ the so-called proper Lorentz group Spin$^+(1,n),$ for the study of spherical continuous wavelet transforms (CWT). Our approach is based on the method for construction of general…
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…
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…
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…
The underlying mathematics of the wavelet formalism is a representation of the inhomogeneous Lorentz group or the affine group. Within the framework of wavelets, it is possible to define the ``window'' which allows us to introduce a…
A new construction of a directional continuous wavelet analysis on the sphere is derived herein. We adopt the harmonic scaling idea for the spherical dilation operator recently proposed by Sanz et al. but extend the analysis to a more…
In this paper we formulate a weighted version of minimum problem (1.4) on the sphere and we show that, for $K\le L$, if $\set{\phi_k}^K_{k=1}$ consists of the spherical functions with degree less than $N$ we can localize the points…
A wavelet is a special case of a vector in a separable Hilbert space that generates a basis under the action of a collection, or system, of unitary operators. We will describe the operator-interpolation approach to wavelet theory using the…
The $\alpha$-modulation transform is a time-frequency transform generated by square-integrable representations of the affine Weyl-Heisenberg group modulo suitable subgroups. In this paper we prove new conditions that guarantee the…
In the general context of complex data processing, this paper reviews a recent practical approach to the continuous wavelet formalism on the sphere. This formalism notably yields a correspondence principle which relates wavelets on the…
We consider dual frames generated by actions of countable discrete groups on a Hilbert space. Module frames in a class of modules over a group algebra are shown to coincide with a class of ordinary frames in a representation of the group.…
Using continuous wavelet transform it is possible to construct a regularization procedure for scale-dependent quantum field theory models, which is complementary to functional renormalization group method in the sense that it sums up the…
The general construction of frames of p-adic wavelets is described. We consider the orbit of a mean zero generic locally constant function with compact support (mean zero test function) with respect to the action of the p-adic affine group…
Continuous wavelet transforms arising from the quasiregular representation of a semidirect product of a vector group with a matrix group -- the so-called dilation group -- have been studied by various authors. Recently the attention has…
We provide explicit criteria for wavelets to give rise to frames and atomic decompositions in ${\rm L}^2(\mathbb{R}^d)$, but also in more general Banach function spaces. We consider wavelet systems that arise by translating and dilating the…
We study the construction of Gabor frames and wavelet frames for Weyl-Heisenberg group and extended affine group by using contraction between the affine group and the Weyl-Heisenberg group due to Subag, Baruch, Birman and Mann. Firstly, we…
This paper presents a full catalogue, up to conjugacy and subgroups of finite index, of all matrix groups $H < {\rm GL}(3,\mathbb{R})$ that give rise to a continuous wavelet transform with associated irreducible quasi-regular…
We extend Robertson's theorem to apply to frames generated by the action of a discrete, countable abelian unitary group. Within this setup we use Stone's theorem and the theory of spectral multiplicity to analyze wandering frame…
The continuous wavelet transform has become a widely used tool in applied science during the last decade. In this article we discuss some generalizations coming from actions of closed subgroups of $\mathrm{GL}(n,\mathbb{R})$ acting on…
We present a unitary approach to the construction of representations and intertwining operators. We apply it to the $C^*$-algebras, groups, Gabor type unitary systems and wavelets. We give an application of our method to the theory of…