Related papers: Spherical Covariance Representations

Using some harmonic extensions on the upper-half plane, and probabilistic representations, and curvature-dimension inequalities with some negative dimensions, we obtain some new opimal functional inequalities of the Beckner type for the…

In this work we present a study on the characterization of ordered and disordered hyperuniform point distributions on spherical surfaces. In spite of the extensive literature on disordered hyperuniform systems in Euclidean geometries, to…

Spherical means are well-known useful tool in the theory of partial differential equations with applications to solving hyperbolic and ultrahyperbolic equations and problems of integral geometry, tomography and Radon transforms. We…

We obtain discrete mixture representations for parametric families of probability distributions on Euclidean spheres, such as the von Mises--Fisher, the Watson and the angular Gaussian families. In addition to several special results we…

Motivated by a recent work of Ache and Chang concerning the sharp Sobolev trace inequality and Lebedev-Milin inequalities of order four on the Euclidean unit ball, we derive such inequalities on the Euclidean unit ball for higher order…

Via a covariance representation based on characteristic functions, a known elementary proof of the Gaussian concentration inequality is presented. A few other applications are briefly mentioned.

We consider systems of partial differential equations of the form \begin{equation}\nonumber \left\{ \begin{array}{l} u_{xt}=F\left(u,u_x,v,v_x\right),\\ v_{xt}=G\left(u,u_x,v,v_x\right), \end{array} \right. \end{equation} describing…

Random fields on the sphere play a fundamental role in the natural sciences. This paper presents a simulation algorithm parenthetical to the spectral turning bands method used in Euclidean spaces, for simulating scalar- or vector-valued…

Physicists routinely need probabilistic models for a number of tasks such as parameter inference or the generation of new realizations of a field. Establishing such models for highly non-Gaussian fields is a challenge, especially when the…

We introduce and study covariance fields of distributions on a Riemannian manifold. At each point on the manifold, covariance is defined to be a symmetric and positive definite (2,0)-tensor. Its product with the metric tensor specifies a…

Understanding how particles are arranged on the sphere is not only central to numerous physical, biological, and materials systems but also finds applications in mathematics and in analysis of geophysical and meteorological measurements. In…

Let $G/H$ be a Riemannian homogeneous space. For an orthogonal representation $\phi$ of $H$ on the Euclidean space $\mathbb{R}^{k+1}$, there corresponds the vector bundle $E=G\times_{\phi}\mathbb{R}^{k+1} \to G/H$ with fiberwise inner…

The work develops further the theory of the following inversion problem, which plays the central role in the rapidly developing area of thermoacoustic tomography and has intimate connections with PDEs and integral geometry: {\it Reconstruct…

This paper considers a multivariate spatial random field, with each component having univariate marginal distributions of the skew-Gaussian type. We assume that the field is defined spatially on the unit sphere embedded in $\mathbb{R}^3$,…

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…

For general varifolds in Euclidean space, we prove an isoperimetric inequality, adapt the basic theory of generalised weakly differentiable functions, and obtain several Sobolev type inequalities. We thereby intend to facilitate the use of…

We define spherical diffraction measures for a wide class of weighted point sets in commutative spaces, i.e. proper homogeneous spaces associated with Gelfand pairs. In the case of the hyperbolic plane we can interpret the spherical…

In this work, we study probability functions associated with Gaussian mixture models. Our primary focus is on extending the use of spherical radial decomposition for multivariate Gaussian random vectors to the context of Gaussian mixture…

It was proved in the first part of this work \cite{0} that Stolarsky's invariance principle, known previously for point distributions on the Euclidean spheres \cite{33}, can be extended to the real, complex, and quaternionic projective…

We study covariant differential calculus on the quantum spheres S_q^2N-1. Two classification results for covariant first order differential calculi are proved. As an important step towards a description of the noncommutative geometry of the…