Related papers: Oversampling generates super-wavelets
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 establish system of equations for single function normalized tight frame wavelets with compact supports associated with $2\times 2$ expansive integral matrices in $L^2(\R^2)$.
In this paper, an algorithm based on polyphase matrix for constructing a pair of orthogonal wavelet frames is suggested, and a general form for all orthogonal tight wavelet frames on local fields of positive characteristic is described.…
The aim of this paper is to extend two results from the Paley--Wiener setting to more generalmodel spaces. The first one is an analogue of the oversampling Shannon sampling formula. The second one is a version of the Donoho--Logan Large…
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 show that a class of de Branges spaces, generated by means of generalized Fourier transforms associated with perturbed Bessel differential equations, has the properties of oversampling and aliasing.
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…
A theory of double affine and special double affine bundles, i.e. differential manifolds with two compatible (special) affine bundle structures, is developed as an affine counterpart of the theory of double vector bundles. The motivation…
Dual pseudo splines constitute a new class of refinable functions with B-splines as special examples, which was introduced in \cite{DHSS}. In this paper, we shall construct Riesz wavelet associated with dual pseudo splines. Furthermore, we…
We propose a superlens formed by an ultra-dense array of crossed metallic wires. It is demonstrated that due to the anomalous interaction between crossed wires, the structured substrate is characterized by an anomalously high index of…
In this article, we present a constructive method for computing the frame coefficients of finite wavelet frames over prime fields using tools from computational harmonic analysis and group theory.
We observe enhanced second-harmonic generation in monolayer graphene in the presence of an ultra-strong terahertz field pulse with a peak amplitude of 250 kV/cm. This is a strongly nonperturbative regime of light-matter interaction in which…
We discover long-lived (microsecond-scale) optical waveguiding in the wake of atmospheric laser filaments. We also observe the formation and then outward propagation of the consequent sound wave. These effects may be used for remote…
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…
The angular spectrum theory is applied to the nonlinear harmonic generation process in optical superlattices. Several explicit and analytical structure functions are deduced to design optical superlattices for various purposes. Employing…
Let $a$, $b$ be two fixed positive constants. A function $g\in L^2({\mathbb R})$ is called a \textit{mother Weyl-Heisenberg frame wavelet} for $(a,b)$ if $g$ generates a frame for $L^2({\mathbb R})$ under modulates by $b$ and translates by…
Supersymmetry predicts multiple flat directions, some of which carry a net baryon or lepton number. Condensates in such directions form during inflation and later fragment into Q-balls, which can become the building blocks of primordial…
Moir\'e superlattices comprised of stacked two-dimensional materials present a versatile platform for engineering and investigating new emergent quantum states of matter. At present, the vast majority of investigated systems have long…
We use curvature decompositions to construct generating sets for the space of algebraic curvature tensors and for the space of tensors with the same symmetries as those of a torsion free, Ricci symmetric connection; the latter naturally…
The purpose of this paper is to join two different threads of the recent literature on random fields on the sphere, namely the statistical analysis of higher order angular power spectra on one hand, and the construction of second-generation…