Related papers: Harmonic Singular Integrals and Steerable Wavelets…
In this paper we formulate a weighted version of minimum problem (1.4) on the sphere and we show that, for $K\le L$, if $\set{\phi_k}^K_{k=1}$ consists of the spherical functions with degree less than $N$ we can localize the points…
We introduce a highly-parallelizable architecture for estimating parameters of compact binary coalescence using gravitational-wave data and waveform models. Using a spherical harmonic mode decomposition, the waveform is expressed as a sum…
We introduce orthogonal ring patterns in the 2-sphere and in the hyperbolic plane, consisting of pairs of concentric circles, which generalize circle patterns. We show that their radii are described by a discrete integrable system. This is…
In this work, we are interested in the differential geometry of curves in the simply isotropic and pseudo-isotropic 3-spaces, which are examples of Cayley-Klein geometries whose absolute figure is given by a plane at infinity and a…
We consider Wave Maps into the sphere and give a new proof of small data global well-posedness and scattering in the critical Besov space, in any space dimension $n \geq 2$. We use an adapted version of the atomic space $U^2$ as the single…
This paper explores woven frames in separable Hilbert spaces with an initial focus on the finite-dimensional case. We begin by simplifying the problem to bases, for which we obtain a unique characterization. We establish a condition that is…
We reduce the equations governing the spherically symmetric perturbations of static spherically symmetric solutions of the Einstein-Vlasov system (with either massive or massless particles) to a single stratified wave equation…
With the aim of constructing a biologically plausible model of machine listening, we study the representation of a multicomponent stationary signal by a wavelet scattering network. First, we show that renormalizing second-order nodes by…
A special class of integrable nonlinear differential equations related to A.III-type symmetric spaces and having additional reductions are analyzed via the inverse scattering method (ISM). Using the dressing method we construct two classes…
We study the construction of nonuniform tight wavelet frames for the Lebesgue space $L^2(\mathbb{R})$, where the related translation set is not necessary a group. The main purpose of this paper is to prove the unitary extension principle…
Intraoperative 2D/3D registration aligns preoperative 3D volumes with real-time 2D radiographs, enabling accurate localization of instruments and implants. A recent fully differentiable similarity learning framework approximates geodesic…
We present a generic scheme to construct corrected trapezoidal rules with spectral accuracy for integral operators with weakly singular kernels in arbitrary dimensions. We assume that the kernel factorization of the form,…
We develop a geometric framework for the numerical integration of mechanical systems evolving on manifolds. After briefly reviewing classical numerical methods and highlighting their limitations and shortcomings in non-flat (non-Euclidean)…
We consider integrals of spherical harmonics with Fourier exponents on the sphere $S^n ,\, n \geq 1$. Such transforms arise in the framework of the theory of weighted Radon transforms and vector diffraction in electromagnetic fields theory.…
We propose a numerical algorithm for backward stochastic differential equations based on time discretization and trigonometric wavelets. This method combines the effectiveness of Fourier-based methods and the simplicity of a wavelet-based…
In this paper, we present a theoretical analysis of separating images consisting of pointlike and $C^{ \beta}$-curvelike structures, where $\beta \in (1,2] $. Our approach is based on $l_1$-minimization, in which the sparsity of the desired…
This paper considers large-scale simulations of wave propagation phenomena. We argue that it is possible to accurately compute a wavefield by decomposing it onto a largely incomplete set of eigenfunctions of the Helmholtz operator, chosen…
The decomposition of the polynomials on the quaternionic unit sphere in $\Hd$ into irreducible modules under the action of the quaternionic unitary (symplectic) group and quaternionic scalar multiplication has been studied by several…
To derive the convergence field from the gravitational shear (gamma) of the background galaxy images, the classical methods require a convolution of the shear to be performed over the entire sky, usually expressed thanks to the Fast Fourier…
Two scaling functions $\varphi_A$ and $\varphi_B$ for Parseval frame wavelets are algebraically isomorphic, $\varphi_A \simeq \varphi_B$, if they have matching solutions to their (reduced) isomorphic systems of equations. Let $A$ and $B$ be…