Related papers: Harmonic Singular Integrals and Steerable Wavelets…
We present a method to combine two periodic lattice wave-fields to generate a complex dual lattice wave-field which could be employed for microfabrication of corresponding 2D dual lattice structures. Since the addition of two periodic…
Spatial sound field interpolation relies on suitable models to both conform to available measurements and predict the sound field in the domain of interest. A suitable model can be difficult to determine when the spatial domain of interest…
Based on the shearlet transform we present a general construction of continuous tight frames for $L^2(\mathbb{R}^2)$ from any sufficiently smooth function with anisotropic moments. This includes for example compactly supported systems,…
The control of wave scattering in complex non-Hermitian settings is an exciting subject -- often challenging the creativity of researchers and stimulating the imagination of the public. Successful outcomes include invisibility cloaks,…
Seismic waves are the most sensitive probe of the Earth's interior we have. With the dense data sets available in exploration, images of subsurface structures can be obtained through processes such as migration. Unfortunately, relating…
Pressing questions in cosmology such as the nature of dark matter and dark energy can be addressed using large galaxy surveys, which measure the positions, properties and redshifts of galaxies in order to map the large-scale structure of…
We study the dynamical symmetries of a class of two-dimensional superintegrable systems on a 2-sphere, obtained by a procedure based on the Marsden-Weinstein reduction, by considering its shape-invariant intertwining operators. These are…
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…
The computation of the symmetric regularized-long-wave (SRLW) equation, which describes weekly nonlinear ion acoustic and space-charge waves, is dealt with in this paper. The numerical scheme to be proposed applies the Fourier…
We obtain a characterization of all wavelets leading to analytic wavelet transforms (WT). The characterization is obtained as a by-product of the theoretical foundations of a new method for wavelet phase reconstruction from magnitude-only…
Learning physical simulations has been an essential and central aspect of many recent research efforts in machine learning, particularly for Navier-Stokes-based fluid mechanics. Classic numerical solvers have traditionally been…
We propose a high-precision numerical quadrature framework based on local Fourier extension (LFE) approximations. The method constructs, on each subinterval, a truncated-SVD stabilized local Fourier continuation of the integrand on an…
A method is described by which a function defined on a cubic grid (as from a finite difference solution of a partial differential equation) can be resolved into spherical harmonic components at some fixed radius. This has applications to…
Wavelets are known to be closely related to atomic orbital. A new approach of 2D, 3D and multidimensional wavelet system is proposed from a paralell with anti-symmetric systems of several isolated particles. The theory of fermionic states…
In this paper, we study the convolution structure in the special affine Fourier domain to combine the advantages of the well known special affine Fourier and wavelet transforms into a novel integral transform coined as special affine…
Gabardo and Nashed have studied nonuniform wavelets based on the theory of spectral pairs for which the associated translation set $\Lambda =\left\{ 0,r/N\right\}+2\,\mathbb Z$ is no longer a discrete subgroup of $\mathbb R$ but a spectrum…
We construct a family of frames describing Sobolev norm and Sobolev seminorm of the space $H^s(\mathbb{R}^d)$. Our work is inspired by the Discrete Orthonormal Stockwell Transform introduced by R.G. Stockwell, which provides a…
Lichnerowicz's algebra of differential geometric operators acting on symmetric tensors can be obtained from generalized geodesic motion of an observer carrying a complex tangent vector. This relation is based upon quantizing the classical…
We consider wavelets in L^2(R^d) which have generalized multiresolutions. This means that the initial resolution subspace V_0 in L^2(R^d) is not singly generated. As a result, the representation of the integer lattice Z^d restricted to V_0…
We introduce a new concept of the so-called {\it composite wavelet transforms}. These transforms are generated by two components, namely, a kernel function and a wavelet function (or a measure). The composite wavelet transforms and the…