Related papers: On construction of multivariate symmetric MRA-base…
We construct spherical wavelets based on approximate identities that are directional, i.e. not rotation-invariant, and have an adaptive angular selectivity. The problem of how to find a proper representation of distinct kinds of details of…
This paper is concerned with orthonormal systems in real intervals, given with zero Dirichlet boundary conditions. More specifically, our interest is in systems with a skew-symmetric differentiation matrix (this excludes orthonormal…
A well known numerical task is the inversion of large symmetric tridiagonal Toeplitz matrices, i.e., matrices whose entries equal $a$ on the diagonal and $b$ on the extra diagonals ($a, b\in \mathbb R$). The inverses of such matrices are…
Which convex subsets of the complex plane are the numerical range W(A of some matrix A? This paper gives a precise characterization of these sets. In addition to this we show that for any A there exists a symmetric matrix B of the same size…
In this paper, Meyer wavelets with an arbitrary integer scaling factor $N>2$ are defined using wavelets with multiple scaling factors $MN>2$. Expressions for frequency functions of wavelets and corresponding filters are obtained.
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…
In a previous paper we have introduced a new class of radial basis functions that are powerful means to approximate functions by quasi-interpolation. In this article we extend the results to create new ways of approximating functions by…
In this paper, we completely solve the matrix extension problem with symmetry and provide a step-by-step algorithm to construct such a desired matrix $\mathsf{P}_e$ from a given matrix $\mathsf{P}$. Furthermore, using a cascade structure,…
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…
Kernel matrices are a key quantity in kernel-based approximation, and important properties such as stability and algorithmic convergence can be analyzed with their help. In this work we refine a multivariate Ingham-type theorem, which is…
In the paper, we consider bivariate isotropic dilation matrices that are similar (up to constant factors) to rotation matrices; and we show that, in this case, the two-scale relation can be considered also as the relation between not only…
Here we present a method of constructing steerable wavelet frames in $L_2(\mathbb{R}^d)$ that generalizes and unifies previous approaches, including Simoncelli's pyramid and Riesz wavelets. The motivation for steerable wavelets is the need…
Wavelet frames for $L^2({\mathbb R})$ can be characterized by means of spectral techniques. This work uses spectral formulas to determine all the tight wavelet frames for $L^2({\mathbb R})$ with a fixed finite number of generators of…
In the literature, few constructions of $n$-variable rotation symmetric bent functions have been presented, which either have restriction on $n$ or have algebraic degree no more than $4$. In this paper, for any even integer $n=2m\ge2$, a…
We construct directional wavelet systems that will enable building efficient signal representation schemes with good direction selectivity. In particular, we focus on wavelet bases with dyadic quincunx subsampling. In our previous work, We…
We establish new quantitative estimates for general systems of functions with wavelet-type dyadic structure. These estimates are applied to obtain the optimal growth of various types of Weyl multipliers for certain wavelet-type systems.…
Samplets are data adapted multiresolution analyses of localized discrete signed measures. They can be constructed on scattered data sites in arbitrary dimension such that they exhibit vanishing moments with respect to any prescribed set of…
Homogeneous wavelets and framelets have been extensively investigated in the classical theory of wavelets and they are often constructed from refinable functions via the multiresolution analysis. On the other hand, nonhomogeneous wavelets…
In this paper, we study scalar multivariate non-stationary subdivision schemes with integer dilation matrix M=mI, m >=2, and present a general approach for checking their convergence and for determining their H\"older regularity. The…
To every subspace arrangement X we will associate symmetric functions P[X] and H[X]. These symmetric functions encode the Hilbert series and the minimal projective resolution of the product ideal associated to the subspace arrangement. They…