Related papers: Poisson wavelets on $n$-dimensional spheres
Directional Poisson wavelets, being directional derivatives of Poisson kernel, are introduced on $n$-dimensional spheres. It is shown that, slightly modified and together with another wavelet family, they are an admissible wavelet pair…
The paper shows that under some mild conditions $n$-dimensional spherical wavelets derived from approximate identities build semi-continuous frames. Moreover, for sufficiently dense grids Poisson wavelets on $n$-dimensional spheres…
In this paper, we are concerned with $n$-dimensional spherical wavelets derived from the theory of approximate identities. For nonzonal bilinear wavelets introduced by Ebert \emph{et al.} in 2009 we prove isometry and Euclidean limit…
We present a method of solving partial differential equations on the $n$-dimensional unit sphere using methods based on the continuous wavelet transform derived from approximate identities. We give an explicit analytical solution to the…
We compute explicit upper bounds on the distance between the law of a multivariate Gaussian distribution and the joint law of wavelets/needlets coefficients based on a homogeneous spherical Poisson field. In particular, we develop some…
In the present paper, multiscale systems of polynomial wavelets on an n-dimensional sphere are constructed. Scaling functions and wavelets are investigated,and their reproducing and localization properties and positive definiteness are…
In the present paper, a construction of spin weighted spherical wavelets is presented. It is based on approximate identities, the wavelets are defined for a continuous set of parameters, and the wavelet transform is invertible directly by…
Many applications of interest involve data that can be analyzed as unit vectors on a d-dimensional sphere. Specific examples include text mining, in particular clustering of documents, biology, astronomy and medicine among others. Previous…
The major goal of the paper is to prove that discrete frames of (directional) wavelets derived from an approximate identity exist. Additionally, a kind of energy conservation property is shown to hold in the case when a wavelet family is…
In this paper we first describe the geometry of the Newton polyhedra of polynomials invariant under certain linear Hamiltonian circle actions. From the geometry of the polyhedra, various Poisson structures on the orbit spaces of the actions…
We show that results of a simple dynamical gedanken experiment interpreted according to standard Newton's gravitational theory, may reveal that three-dimensional space is curved. The experiment may be used to reconstruct the curved geometry…
Project a collection of points on the high-dimensional sphere onto a random direction. If most of the points are sufficiently far from one another in an appropriate sense, the projection is locally close in distribution to the Poisson point…
In this paper, quantitative bounds in high-frequency central limit theorems are derived for Poisson based $U$-statistics of arbitrary degree built by means of wavelet coefficients over compact Riemannian manifolds. The wavelets considered…
We provide an integral formula for the Poisson kernel of half-spaces for Brownian motion in real hyperbolic space $\H^n$. This enables us to find asymptotic properties of the kernel. Our starting point is the formula for its Fourier…
Consider a second-order elliptic operator $L$ in the half-plane $\mathbb R \times (0, \infty)$ with coefficients depending only on the second coordinate. The Poisson kernel for $L$ is used in the representation of positive $L$-harmonic…
We propose a method of solving partial differential equations on the $n$-dimen\-sional unit sphere with methods based on the continuous wavelet transform derived from approximate identities.
Flexible bandwidth needlets provide a localized multiscale framework with scale-adaptive frequency resolution, enabling effective analysis of spherical Poisson random fields exhibiting spatial inhomogeneity and scale variation. We establish…
We study a class of localized solutions of the wave equation, called eigenwavelets, obtained by extending its fundamental solutions to complex spacetime in the sense of hyperfunctions. The imaginary spacetime variables y, which form a…
Scale-discretised wavelets yield a directional wavelet framework on the sphere where a signal can be probed not only in scale and position but also in orientation. Furthermore, a signal can be synthesised from its wavelet coefficients…
We construct a directional spin wavelet framework on the sphere by generalising the scalar scale-discretised wavelet transform to signals of arbitrary spin. The resulting framework is the only wavelet framework defined natively on the…