Related papers: A Note on Spherical Needlets
In a previous paper we have introduced a new class of radial basis functions that are powerful means to approximate functions by quasi-interpolation. In this article we extend the results to create new ways of approximating functions by…
The transport of charged particles or photons in a scattering medium can be modelled with a Boltzmann equation. The mathematical treatment for scattering in such scenarios is often simplified if evaluated in a frame where the scattering…
In this work, shells are mathematically constructed by applying the cut and paste procedure to D-dimensional spherically symmetric geometries. The weak energy condition for the matter on the shells is briefly analyzed. The dynamical…
A wavelet is a localized function having a prescribed number of vanishing moments. In this correspondence, we provide precise arguments as to why the Hilbert transform of a wavelet is again a wavelet. In particular, we provide sharp…
Spherical $t$-designs are finite point sets on the unit sphere that enable exact integration of polynomials of degree at most $t$ via equal-weight quadrature. This concept has recently been extended to spherical $t$-design curves by the use…
Spin-weighted spheroidal harmonics are useful in a variety of physical situations, including light scattering, nuclear modeling, signal processing, electromagnetic wave propagation, black hole perturbation theory in four and higher…
A method is described by which a function defined on a cubic grid (as from a finite difference solution of a partial differential equation) can be resolved into spherical harmonic components at some fixed radius. This has applications to…
The spatial coherence of an atomic wavepacket can be detected in the scattered photons, even when the center-of-mass motion is in the quantum coherent superposition of two distant, non-overlapping wave packets. Spatial coherence manifests…
The study of spherical harmonics in superspace, introduced in [J. Phys. A: Math. Theor. 40 (2007) 7193-7212], is further elaborated. A detailed description of spherical harmonics of degree k is given in terms of bosonic and fermionic…
This paper presents a method for the approximation of harmonic potentials that combines downward continuation of globally available data on a sphere $\Omega_R$ of radius $R$ (e.g., a satellite's orbit) with locally available data on a…
This is the first article in a series of three dealing with the exploitation of speckle for imaging purposes. Speckle is the complex interference wave-field produced by a random distribution of un-resolved scatterers. In this paper, we show…
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…
The structural properties of packed soft-core particles provide a platform to understand the cross-pollinated physical concepts in solid-state- and soft-matter physics. Confined on spherical surface, the traditional differential geometry…
In this work, phase singularities embedded in a wavepacket are shown to act as sources of atypical localized oscillations when the packet interacts with a linear system. We refer to these oscillations as \textit{chirpons}, since they arise…
Light scattering in random media is usually considered within the framework of the three-dimensional Anderson universality class, with modifications for the vector nature of electromagnetic waves. We propose that the linear dispersiveness…
Normalized wave packets express particles in nature. Their sizes are determined by their interactions with matter, and depend on environments. Nevertheless, these characterize scatterings processes in realistic situations, and govern the…
Spin-weighted spheroidal harmonics play a central role in the mathematical description of diverse physical phenomena, including black-hole perturbation theory and wave scattering. We present a novel and compact derivation of the asymptotic…
Entanglement is one of the most fascinating properties of quantum mechanical systems; when two particles are entangled the measurement of the properties of one of the two allows to instantaneously know the properties of the other, whatever…
Wavelets are known to be closely related to atomic orbital. A new approach of 2D, 3D and multidimensional wavelet system is proposed from a paralell with anti-symmetric systems of several isolated particles. The theory of fermionic states…
This short paper is concerned with the use of spherical t-designs as optimal designs for the spherical harmonic regression model in three dimensions over a range of specified criteria. The nature of the designs is explored and their…