相关论文: An equivalence relation on wavelets in higher dime…
An examination of the translation invariance of $V_0$ under dyadic rationals is presented, generating a new equivalence relation on the collection of wavelets. The equivalence classes under this relation are completely characterized in…
We study the action of translation operators on wavelet subspaces. This action gives rise to an equivalence relation on the set of all wavelets. We show by explicit construction that each of the associated equivalence classes is non-empty.
We prove three results on wavelets for the Hardy space H^2(\R). All wavelets constructed so far for H^2(\R) are MSF wavelets. We construct a family of H^2-wavelets which are not MSF. An equivalence relation on H^2-wavelets is introduced and…
All wavelets can be associated to a multiresolution like structure, i.e. an incr easing sequence of subspaces of L^2(R). We consider the interaction of a wavel et and the translation operator in terms of which of the subspaces in this multi…
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…
For an arbitrary matrix dilation, any integer n and any integer/semi-integer c, we describe all masks that are symmetric with respect to the point c and have sum rule of order n. For each such mask, we give explicit formulas for wavelet…
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…
We solve the wavelet set existence problem. That is, we characterize the full-rank lattices $\Gamma\subset \mathbb R^n$ and invertible $n \times n$ matrices $A$ for which there exists a measurable set $W$ such that $\{W + \gamma: \gamma \in…
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…
In continuous-time wavelet analysis, most wavelet present some kind of symmetry. Based on the Fourier and Hartley transform kernels, a new wavelet multiresolution analysis is proposed. This approach is based on a pair of orthogonal wavelet…
Let R be an associative ring with identity. We introduce an equivalence relation on the class of Wakamatsu tilting right R modules. By using this equivalence relation, we extend the Mantese Reiten theorems from the setting of Artin algebras…
New elliptic cylindrical wavelets are introduced, which exploit the relationship between analysing filters and Floquet's solution of Mathieu differential equations. It is shown that the transfer function of both multiresolution filters is…
We establish system of equations for single function normalized tight frame wavelets with compact supports associated with $2\times 2$ expansive integral matrices in $L^2(\R^2)$.
We investigate the connection between radix representations for Z^n and self-affine tilings of R^n. We apply our results to show that Haar-like multivariable wavelets exist for all dilation matrices that are sufficie
This note introduces a new family of wavelets and a multiresolution analysis, which exploits the relationship between analysing filters and Floquet's solution of Mathieu differential equations. The transfer function of both the detail and…
In this article, we present a simple criterion for checking whether a one-parameter matrix group of dilations admits a continuous wavelet. This criterion involves only checking that the eigenvalues of the symmetric part of the matrix have…
We introduce a method to construct large classes of MSF wavelets of the Hardy space H^2(\R) and symmetric MSF wavelets of L^2(\R), and discuss the classification of such sets. As application, we show that there are uncountably many wavelet…
We lift the constraint of a diagonal representation of the Hamiltonian by searching for square integrable bases that support an infinite tridiagonal matrix representation of the wave operator. The class of solutions obtained as such…
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…
In this paper we explore a class of equivalence relations over $\N^\ast$ from which is constructed a sequence of symetric matrices related to the Mertens function. From numerical experimentations we suggest a conjecture, about the growth of…