Related papers: Some characterizations of the spherical harmonics …
We derive new relationships expressing solid spherical harmonics as series of toroidal harmonics and vice versa. The expansions include regular and irregular spherical harmonics, ring and axial toroidal harmonics of even and odd parity…
Within the scope of a spherically symmetric space-time we study the role of different types of matter in the formation of different configurations with spherical symmetries. Here we have considered matter with barotropic equation of state,…
The article contains several observations on spherical harmonics and their nodal sets: a construction for harmonics with prescribed zeroes; a kind of canonical representation of this type for harmonics on $\bbS^2$; upper and lower bounds…
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…
An expression for the joint probability distribution of the principal curvatures at an arbitrary point in the ensemble of isosurfaces defined on isotropic Gaussian random fields on Rn is derived. The result is obtained by deriving symmetry…
We give a complete classification of Riemannian and Lorentzian surfaces of arbitrary codimension in a pseudo-sphere whose pseudo-spherical Gauss maps are of 1-type or, in particular, harmonic. In some cases a concrete global classification…
This survey is devoted to recent developments in the statistical analysis of spherical data, with a view to applications in Cosmology. We will start from a brief discussion of Cosmological questions and motivations, arguing that most…
In this paper we investigate gravitationally bound, spherically symmetric equilibrium configurations consisting of ordinary (polytropic) matter nonminimally coupled to an external chameleon scalar field. We show that this system has static,…
The orthonormal set of Spherical Harmonics provides a natural way of expanding whole sky redshift and peculiar velocity surveys.
In this paper, we investigate the dynamics of both free particle and isotropic harmonic oscillator constrained to move on a spheroidal surface using two consecutive projections: a projection onto a sphere surface followed by the gnomonic…
The objective of this paper is to characterize harmonic Hardy spaces and a boundary behavior of harmonic functions on a smooth domain in real Euclidean space.
We study the weak convergence (in the high-frequency limit) of the parameter estimators of power spectrum coefficients associated with Gaussian, spherical and isotropic random fields. In particular, we introduce a Whittle-type approximate…
We reconsider some subtle points concerning the relativistic treatment of the gravitational fields generated by spherically symmetric structures.
We apply the topological quantization method to some gravitational fields which can be represented as generalized harmonic maps. This representation extends the well-known concept of harmonic maps and allows us to describe some solutions to…
In this pedagogically structured article, we describe a generalized harmonic formulation of the Einstein equations in spherical symmetry which is regular at the origin. The generalized harmonic approach has attracted significant attention…
We study general models of random fields associated with non-local equations in time and space. We discuss the properties of the corresponding angular power spectrum and find asymptotic results in terms of random time changes.
This is a direct computation of the spectral representation of homogeneous spin-weighted spherical random fields with arbitrary integer spin. It generalises known results from Cosmology for the spin-2 Cosmic Microwave Background…
We investigate the general relativistic phase of an electromagnetic wave as it propagates in the gravitational field of the Earth, which is modeled as an isolated, weakly aspherical gravitating body. We introduce coordinate systems to…
In this article, we present a space-frequency theory for spherical harmonics based on the spectral decomposition of a particular space-frequency operator. The presented theory is closely linked to the theory of ultraspherical polynomials on…
We study the sample paths properties of Operator scaling Gaussian random fields. Such fields are anisotropic generalizations of anisotropic self-similar random fields as anisotropic Fractional Brownian Motion. Some characteristic properties…