Related papers: On a spherical code in the space of spherical harm…
We introduce a framework for constructing quantum codes defined on spheres by recasting such codes as quantum analogues of the classical spherical codes. We apply this framework to bosonic coding, obtaining multimode extensions of the cat…
Laplacian eigenmodes on homogeneous Clifford--Klein factors of the three--sphere are obtained as pullbacks of harmonics on the orbifolded two--sphere using the Hopf map. A method of obtaining these polyhedral, or crystal, harmonics using…
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.
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,…
We give a brief account of two recent applications of the harmonic superspace method: (i) an off-shell description of torsionful $(4,4)$ supersymmetric $2D$ sigma models in the framework of $SU(2)\times SU(2)$ harmonic superspace and (ii)…
We present some addition theorems for spin-weighted spherical harmonics, generalizing previous results for scalar (spin-zero) spherical harmonics. These addition theorems involve sums over the azimuthal quantum number of products of two…
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…
Spherical harmonics (SH) have been extensively used as a basis for analyzing the morphology of particles in granular mechanics. The use of SH is facilitated by mapping the particle coordinates onto a unit sphere, in practice often a…
We present a new spectral scheme for analysing functions of half-integer spin-weight on the $2$-sphere and demonstrate the stability and convergence properties of our implementation. The dynamical evolution of the Dirac equation on a…
Subspace codes have received an increasing interest recently due to their application in error-correction for random network coding. In particular, cyclic subspace codes are possible candidates for large codes with efficient encoding and…
By the collective name of {\it lattice counting} we refer to a setup introduced in Duke-Rudnick-Sarnak that aim to establish a relationship between arithmetic and randomness in the context of affine symmetric spaces. In this paper we extend…
An algorithm is presented for numerical computation of choreographies in the plane in a Newtonian potential and on the sphere in a cotangent potential. It is based on stereographic projection, approximation by trigonometric polynomials, and…
We present a comprehensive construction of scalar, vector and tensor harmonics on maximally symmetric three-dimensional spaces. Our formalism relies on the introduction of spin-weighted spherical harmonics and a generalized helicity basis…
In this paper, we determine the spherical functions of positive type on the inductive limit space of square complex matrices.
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…
We generalize the spherical harmonics for l=1 and give the differential equation that the generalized forms satisfy. The new forms have an obvious interpretation in the context of quantum mechanics.
This paper gives a method to construct rigid spaces, which is similar to the method used to construct toric schemes.
Harmonic superspaces for spacetimes of dimension $d\leq 3$ are constructed. Some applications are given.
We apply the semidefinite programming approach developed in arxiv:math.MG/0608426 to obtain new upper bounds for codes in spherical caps. We compute new upper bounds for the one-sided kissing number in several dimensions where we in…
We introduce a new numerically stable method for constructing superoscillatory wave forms inan arbitrary number of dimensions. The method allows the construction of superoscillatory square-integrable functions that match any desired smooth…