97 citations · 163 across the 13 of their papers we have counts for
16 papers
Riesz Energy with a Radial External Field: When is the Equilibrium Support a Sphere?
Djalil Chafaï, Ryan W. Matzke, Edward B. Saff +2
We consider Riesz energy problems with radial external fields. We study the question of whether or not the equilibrium is the uniform distribution on a sphere. We develop general n…
Removing the mask -- reconstructing a scalar field on the sphere from a masked field
Jan Hamann, Quoc Thong Le Gia, Ian H. Sloan +1
The paper analyses a spectral approach to reconstructing a scalar field on the sphere, given only information about a masked version of the field together with precise information…
Needlets Liberated
Johann S. Brauchart, Peter J. Grabner, Ian H. Sloan +1
Spherical needlets were introduced by Narcowich, Petrushev, and Ward to provide a multiresolution sequence of polynomial approximations to functions on the sphere. The needlet cons…
Threshold condensation to singular support for a Riesz equilibrium problem
Djalil Chafaï, Edward B. Saff, Robert S. Womersley
We compute the equilibrium measure in dimension d=s+4 associated to a Riesz s-kernel interaction with an external field given by a power of the Euclidean norm. Our study reveals th…
On the solution of a Riesz equilibrium problem and integral identities for special functions
Djalil Chafaï, Edward B. Saff, Robert S. Womersley
The aim of this note is to provide a full space quadratic external field extension of a classical result of Marcel Riesz for the equilibrium measure on a ball with respect to Riesz…
A New Probe of Gaussianity and Isotropy applied to the CMB Maps
J. Hamann, Q. T. Le Gia, I. H. Sloan +2
We introduce a new mathematical tool (a direction-dependent probe) to analyse the randomness of purported isotropic Gaussian random fields on the sphere. We apply the probe to asse…
Sparse Isotropic Regularization for Spherical Harmonic Representations of Random Fields on the Sphere
Quoc T. Le Gia, Ian H. Sloan, Robert S. Womersley +1
This paper discusses sparse isotropic regularization for a random field on the unit sphere in , where the field is expanded in terms of a spherical h…
Efficient Spherical Designs with Good Geometric Properties
Robert S. Womersley
Spherical -designs on provide nodes for an equal weight numerical integration rule which is exact for all spherical polynomials of de…
Logarithmic and Riesz Equilibrium for Multiple Sources on the Sphere --- the Exceptional Case
Johann S. Brauchart, Peter D. Dragnev, Edward B. Saff +1
We consider the minimal discrete and continuous energy problems on the unit sphere in the Euclidean space in the presence of an external field due…
Needlet approximation for isotropic random fields on the sphere
Quoc T. Le Gia, Ian H. Sloan, Yu Guang Wang +1
In this paper we establish a multiscale approximation for random fields on the sphere using spherical needlets --- a class of spherical wavelets. We prove that the semidiscrete nee…
Random Point Sets on the Sphere --- Hole Radii, Covering, and Separation
Johann S. Brauchart, Alexander B. Reznikov, Edward B. Saff +3
Geometric properties of random points distributed independently and uniformly on the unit sphere with respect to surface area measure ar…
Riemann localisation on the sphere
Yu Guang Wang, Ian H. Sloan, Robert S. Womersley
This paper first shows that the Riemann localisation property holds for the Fourier-Laplace series partial sum for sufficiently smooth functions on the two-dimensional sphere, but…
Fully discrete needlet approximation on the sphere
Yu Guang Wang, Quoc T. Le Gia, Ian H. Sloan +1
Spherical needlets are highly localized radial polynomials on the sphere , , with centers at the nodes of a suitable cubature rule.…
Covering of spheres by spherical caps and worst-case error for equal weight cubature in Sobolev spaces
Johann S. Brauchart, Josef Dick, Edward B. Saff +3
We prove that the covering radius of an -point subset of the unit sphere is bounded above by a power of the worst-case error for equal weight cubatur…
QMC designs: optimal order Quasi Monte Carlo Integration schemes on the sphere
Johann S. Brauchart, Edward B. Saff, Ian H. Sloan +1
We study equal weight numerical integration, or Quasi Monte Carlo (QMC) rules, for functions in a Sobolev space with smoothness parameter defined over the unit s…
Wendland functions with increasing smoothness converge to a Gaussian
A. Chernih, I. H. Sloan, R. S. Womersley
The Wendland functions are a class of compactly supported radial basis functions with a user-specified smoothness parameter. We prove that with a linear change of variables, both t…