Related papers: Matrix Valued Spherical Functions Associated to th…
This paper deals with some simple results about spherical functions of type $\delta$, namely new integral formulas, new results about behavior at infinity and some facts about the related $C_\sigma$ functions.
We obtain new inequalities for certain hypergeometric functions. Using these inequalities, we deduce estimates for the hyperbolic metric and the induced distance function on a certain canonical hyperbolic plane domain.
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…
In this paper, we study the Dirichlet series that enumerates proper equivalence classes of full-rank sublattices of a given quadratic lattice in a hyperbolic plane -- that is, a nondegenerate isotropic quadratic space of dimension $2$. We…
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…
Explicit expressions for associated spherical functions of $SO(p,q)$ matrix groups are obtained using a generalized hypergeometric series of two variables.
The relation between solutions to Helmholtz's equation on the sphere $S^{n-1}$ and the $[{\gr sl}(2)]^n$ Gaudin spin chain is clarified. The joint eigenfuctions of the Laplacian and a complete set of commuting second order operators…
We study special functions on euclidean spaces from the viewpoint of riemannian symmetric spaces. Here the euclidean space $E^n = G/K$ where $G$ is the semidirect product $R^n \cdot K$ of the translation group with a closed subgroup $K$ of…
Spherical representations and functions are the building blocks for harmonic analysis on riemannian symmetric spaces. In this paper we consider spherical functions and spherical representations related to certain infinite dimensional…
The theoretical computing of special values assumed by the hypergeometric functions has a high interest not only on its own, but also in sight of the remarkable implications to both pure Mathematics and Mathematical Physics. Accordingly, in…
We study the Heckman-Opdam hypergeometric functions associated to a root system of type $BC$ and a multiplicity function which is allowed to assume some non-positive values (a standard multiplicity function). For such functions, we obtain…
Basis functions which are invariant under the operations of a rotational point group $G$ are able to describe any 3-D object which exhibits the rotational point group symmetry. However, in order to characterize the spatial statistics of an…
The spectral decomposition for an explicit second-order differential operator $T$ is determined. The spectrum consists of a continuous part with multiplicity two, a continuous part with multiplicity one, and a finite discrete part with…
Y. Hironaka introduced the spherical functions on the p-adic space of Hermitian matrices. For the space of 2\times2 Hermitian matrices, we complete Hironaka's work by also considering the case of a wildly ramified quadratic extension. We…
The main purpose of this paper is to obtain an explicit expression of a family of matrix valued orthogonal polynomials {P_n}_n, with respect to a weight W, that are eigenfunctions of a second order differential operator D. The weight W and…
Let G/K be an irreducible Hermitian symmetric space and let D be a K-invariant domain in G/K. In this paper we characterize several classes of K-invariant plurisubharmonic functions on D in terms of their restrictions to a slice…
We construct new explicit proper r-harmonic functions on the standard n-dimensional sphere S^n and hyperbolic space H^n for any r\ge 1 and n\ge 2.
Matrix elements of spinor and principal series representations of the Lorentz group are studied in the basis of complex angular momentum (helicity basis). It is shown that matrix elements are expressed via hyperspherical functions…
The pseudospherical functions on one-sheet, two-dimensional hyperboloid are discussed. The simplest method of construction of these functions is introduced using the Fock space structure of the representation space of the su(1,1) algebra.…
Homogeneous superspaces arising from the general linear supergroup are studied within a Hopf algebraic framework. Spherical functions on homogeneous superspaces are introduced, and the structures of the superalgebras of the spherical…