Related papers: Spherical functions on $p$-adic homogeneous spaces

A rigorous and powerful theoretical framework is proposed to obtain systems of orthogonal functions (or shape modes) to represent optical surfaces. The method is general so it can be applied to different initial shapes and different…

The $\Theta$-spherical functions generalize the spherical functions on Riemannian symmetric spaces and the spherical functions on non-compactly causal symmetric spaces. In this article we consider the case of even multiplicity functions. We…

Series representations consisting of spherical harmonics are obtained for characteristic exponents and probability density functions of multivariate stable distributions under various conditions. A esult potentially applicable in a…

Let p be a prime. A p-adic functional on a torsion-free abelian group G is a group homomorphism from G to the p-adic integers. The group of all such p-adic functionals is viewed as a p-adic dual group of G, and is studied from the point of…

This paper is a continuation of a previous paper in which the first two authors have introduced the spherical Hecke algebra and the Satake isomorphism for an untwisted affine Kac-Moody group over a non-archimedian local field. In this paper…

We present a systematic analytic study of the $p$-Bessel functions $\mathcal{J}_{\omega,\varphi}^{[p]}$, a novel class of generalized Bessel functions arising from Fourier analysis on planar domains bounded by $p$-circles, including…

We use a form of lifted harmonic analysis to develop a two-dimensional adelic integral representation of the zeta functions of simple arithmetic surfaces. Manipulations of this integral then lead to an adelic interpretation of the so-called…

We give a self-contained presentation of a novel approach to a construction of spherical harmonic expansions on the unit sphere in $\NC^n$. We derive a new formula for coefficients of the expansion of a smooth zonal function defined on the…

Satellites mapping the spatial variations of the gravitational or magnetic fields of the Earth or other planets ideally fly on polar orbits, uniformly covering the entire globe. Thus, potential fields on the sphere are usually expressed in…

We calculate the partition function of a harmonic oscillator with quasi-periodic boundary conditions using the zeta-function method. This work generalizes a previous one by Gibbons and contains the usual bosonic and fermionic oscillators as…

We exhibit a basis for the space of spherical characters of a distinguished supercuspidal representation $\pi$ of a connected reductive $p$-adic group, subject to the assumption that $\pi$ is obtained via induction from a representation of…

We generalize the known constructions of A-hypergeometric functions. In particular, we show that periods of middle dimension on affine or projective complex algebraic varieties are A-hypergeometric functions of coefficients of polynomial…

Whittaker functions are special functions that arise in $p$-adic number theory and representation theory. They may be defined on representations of reductive groups as well as their metaplectic covering groups: fascinatingly, many of their…

In \cite{5} we proved that generically functions defined in any open set can be approximated by a sequense of their pad\'{e} approximants, in the sense of uniform convergence on compacta. In this paper we examine a more particular space,…

We present a unified approach for constructing Slepian functions - also known as prolate spheroidal wave functions - on the sphere for arbitrary tensor ranks including scalar, vectorial, and rank 2 tensorial Slepian functions, using…

We introduce the notion of Gelfand pairs and zonal spherical functions for Iwahori-Hecke algebras.

In this paper, we compare two optimization algorithms using full Hessian and approximation Hessian to obtain numerical spherical designs through their variational characterization. Based on the obtained spherical design point sets, we…

Partial zeta functions of algebraic varieties over finite fields generalize the classical zeta function by allowing each variable to be defined over a possibly different extension field of a fixed finite field. Due to this extra variation…

We write down a one-dimensional integral formula and compute large-n asymptotics for the expectation of the absolute value of the smallest component of a unit vector in n-dimensional Euclidean space. The method is general, and allows to…

We introduce generalized Schur functions and generalized positive functions in setting of slice hyperholomorphic functions and study their realizations in terms of associated reproducing kernel Pontryagin spaces