Boundary value problems on Riemannian Symmetric Spaces of the noncompact Type

TL;DR

This paper characterizes the image of the Poisson transform on boundaries of noncompact Riemannian symmetric spaces using differential equations linked to algebraic ideals, extending understanding of harmonic analysis on these spaces.

Contribution

It provides an explicit description of the Poisson transform's image via differential equations related to minimal polynomial analogues in the universal enveloping algebra.

Findings

Explicit characterization of the Poisson transform's image.

Differential equations corresponding to algebraic ideals.

Connection between harmonic analysis and algebraic structures.

Abstract

We characterize the image of the Poisson transform on any distinguished boundary of a Riemannian symmetric space of the noncompact type by a system of differential equations. The system corresponds to a generator system of a two sided ideals of an universal enveloping algebra, which are explicitly given by analogues of minimal polynomials of matrices.