In this paper we establish a close relationship between the spherical functions of the n-dimensional sphere $S^n\simeq\SO(n+1)/\SO(n)$ and the spherical functions of the n-dimensional real projective space $P^n(\mathbb{R ...

In this article, using the notion of group contraction, we obtain the spherical functions of the strong Gelfand pair (M(n),SO(n)) as an appropriate limit of spherical functions of the strong Gelfand pair (SO(n+1),SO(n)) ...

The tensorial spin-s and the spin weighted spherical harmonics are functions on the sphere which are extremely useful for many calculations in general relativity. These sets of functions constitute two orthonormal bases ...

In this paper, we describe the irreducible spherical functions of fundamentalK-types associated with the pair (G, K) = (SO(n + 1), SO(n)) in terms of matrix hypergeometric functions. The output of this description is that ...

We consider R3 as a homogeneous manifold for the action of the motion group given by rotations and translations. For an arbitrary τ∈ SO(3) ^ , let Eτ be the homogeneous vector bundle over R3 associated with τ. An interesting ...

In a work published in this journal by Z.W. Wang, G.Z. Li, D.R. Guan, X.Z. Yi, and A.J. Lou [J. Colloid Interface Sci. 246 (2002) 302], an iterative method for the determination of the potential around a colloidal particle ...

The properties of excitons formed in spherical quantum dots are studied using the k⋅p method within the Hartree approximation. The spherical quantum dots considered have a central core and several concentric layers of ...

The main purpose of this paper is to compute all irreducible spherical functions on G = SL(2, ℂ) of arbitrary type δ ∈ K̂, where K = SU(2). This is accomplished by associating to a spherical function Φ on G a matrix valued ...

In Part 1 we study the spherical functions on compact symmetric pairs of arbitrary rank under a suitable multiplicity freeness assumption and additional conditions on the branching rules. The spherical functions are taking ...