相关论文: Wavelet filters and infinite-dimensional unitary g…
In this article we show that there exist measurable sets W in the plane with finite measure that tile the plane in a measurable way under the action of a expansive matrix A, an affine Weyl group W, and a full rank lattice G. This note is…
We consider the design of an orthogonal symmetric/antisymmetric multiwavelet from its matrix product filter by matrix spectral factorization (MSF). As a test problem, we construct a simple matrix product filter with desirable properties,…
Let $G={\rm Spec} A$ be a linearly reductive group and let $w_G\in A^*$ be the invariant integral on $G$. We establish the harmonic analysis on $G$ and we compute $w_G$ when $G=Sl_n, Gl_n, O_n, Sp_{2n}$ by geometric arguments and by means…
The Helmholtz equation with variable wavenumbers is challenging to solve numerically due to the pollution effect, which often results in a huge ill-conditioned linear system. In this paper, we present a high-order wavelet Galerkin method to…
In this short note we discuss the interplay between finite Coxeter groups and construction of wavelet sets, generalized multiresolution analysis and sampling.
A complete framework for the linear time-invariant (LTI) filtering theory of bivariate signals is proposed based on a tailored quaternion Fourier transform. This framework features a direct description of LTI filters in terms of their…
The model-independent "box" parameterization of neutrino oscillations is examined. The invariant boxes are the classical amplitudes of the individual oscillating terms. Being observables, the boxes are independent of the choice of…
The purpose of this paper is to investigate the global categorical symmetries that arise when gauging finite higher groups in three or more dimensions. The motivation is to provide a common perspective on constructions of non-invertible…
We develop a general notion of orthogonal wavelets `centered' on an irregular knot sequence. We present two families of orthogonal wavelets that are continuous and piecewise polynomial. We develop efficient algorithms to implement these…
Cluster algebras are a recent topic of study and have been shown to be a useful tool to characterize structures in several knowledge fields. An important problem is to establish whether or not a given cluster algebra is of finite type.…
In this paper, we will introduce a subcategory of totally reflexive modules that have a saturated filtration by other totally reflexive modules. We will prove these are precisely the totally reflexive modules with an upper-triangular…
We use filtrations of the Grassmannian model to produce explicit algebraic formulae for all harmonic maps of finite uniton number from a Riemann surface, and so all harmonic maps from the 2-sphere, to the unitary group for a general class…
We study the relationship between the (1+1)-affine Galilei group and four groups of interest in signal analysis and image processing, viz., the wavelet or the affine group of the line, the Weyl-Heisenberg, the shearlet and the Stockwell…
Recent work introduced a unified framework for steerable and directional wavelets in two and three dimensions that ensures many desirable properties, such as a multi-scale structure, fast transforms, and a flexible angular localization. We…
Motivated by wavelet analysis, we prove that there is a one-to-one correspondence between the following data: Solutions to $R(h)=h$ where $R$ is a certain non-positive Ruelle transfer operator; Operators that intertwine a certain class of…
We study the parameterized complexity of a robust generalization of the classical Feedback Vertex Set problem, namely the Group Feedback Vertex Set problem; we are given a graph G with edges labeled with group elements, and the goal is to…
In this paper, we study nonhomogeneous wavelet systems which have close relations to the fast wavelet transform and homogeneous wavelet systems. We introduce and characterize a pair of frequency-based nonhomogeneous dual wavelet frames in…
Symmetry is one of the significant visual properties inside an image plane, to identify the geometrically balanced structures through real-world objects. Existing symmetry detection methods rely on descriptors of the local image features…
Motivated by the work of Goswami on quantum isometry groups of noncommutative manifolds we define the quantum symmetry group of a unital C*-algebra A equipped with an orthogonal filtration as the universal object in the category of compact…
We use pluriharmonic maps to study representations of fundamental groups of algebraic manifolds. This approach is functorial in the sense that the restriction of such a map to a fiber of a fibration remains pluriharmonic, and on this basis,…