Related papers: Spherical Harmonics in p Dimensions
In this paper we focus on r-geometric polynomials, r-exponential polynomials and their harmonic versions. It is shown that harmonic versions of these polynomials and their generalizations are useful to obtain closed forms of some series…
The notion of spherically symmetric superfunctions as functions invariant under the orthosymplectic group is introduced. This leads to dimensional reduction theorems for differentiation and integration in superspace. These spherically…
P. Baird and the second author studied harmonic morphisms from a three-dimensional simply-connected space form to a surface and obtained a complete local and global classification of them. In this paper, we obtain a description of all…
The main objective of this paper is to give a wide study on the conformable fractional Legendre polynomials (CFLPs). This study is assumed to be a generalization and refinement, in an easy way, of the scalar case into the context of the…
In dimension $n=1$ we obtain $L^{p_1}(\mathbb R) \times\dots\times L^{p_m}(\mathbb R)$ to $L^p(\mathbb R)$ boundedness for the multilinear spherical maximal function in the largest possible open set of indices and we provide counterexamples…
The authors present SHarmonic, a new implementation of the spherical harmonics targeted for electronic-structure calculations. Their approach is to use explicit formulas for the harmonics written in terms of normalized Cartesian…
We find that the solution of the polar angular differential equation can be written as the universal associated Legendre polynomials. Its generating function is applied to obtain an analytical result for a class of interesting integrals…
The connection between spherical harmonics and symmetric tensors is explored. For each spherical harmonic, a corresponding traceless symmetric tensor is constructed. These tensors are then extended to include nonzero traces, providing an…
We derive some identities and relations and extremal problems and minimization and Fourier development involving of integral Legendre polynomials.
Variables adapted to the quantum dynamics of spherically symmetric models are introduced, which further simplify the spherically symmetric volume operator and allow an explicit computation of all matrix elements of the Euclidean and…
We present a classification of all spherical indecomposable representations of classical and exceptional Lie superalgebras. We also include information about stabilizers, symmetric algebras, and Borels for which sphericity is achieved. In…
The number of linear independent algebraic relations among elementary symmetric polynomial functions over finite fields is computed. An algorithm able to find all such relations is described. It is proved that the basis of the ideal of…
Orthogonal polynomials and multiple orthogonal polynomials are interesting special functions because there is a beautiful theory for them, with many examples and useful applications in mathematical physics, numerical analysis, statistics…
We introduce and study higher spherical algebras, an exotic family of finite-dimensional algebras over an algebraically closed field. We prove that every such an algebra is derived equivalent to a higher tetrahedral algebra studied in [7],…
The decomposition of the polynomials on the quaternionic unit sphere in $\Hd$ into irreducible modules under the action of the quaternionic unitary (symplectic) group and quaternionic scalar multiplication has been studied by several…
In this paper, we study non-linear differential equations associated with Legendre polynomials and their applications. From our study of non- linear differential equations, we derive some new and explicit identities for Legendre…
We are interested in the harmonic analysis on $p$-adic homogeneous spaces based on spherical functions. In the present paper, we investigate the space $X$ of unitary hermitian matrices of odd size over a ${\mathfrak p}$-adic field of odd…
This paper investigates the existence, nonexistence, and qualitative properties of p-harmonic functions in the upper half-space $\mathbb{R}^N_+ \, (N \geq 3)$ satisfying nonlinear boundary conditions for $1<p<N$. Moreover, the symmetry of…
A rapid transformation is derived between spherical harmonic expansions and their analogues in a bivariate Fourier series. The change of basis is described in two steps: firstly, expansions in normalized associated Legendre functions of all…
Linear programming (polynomial) techniques are used to obtain lower and upper bounds for the potential energy of spherical designs. This approach gives unified bounds that are valid for a large class of potential functions. Our lower bounds…