Holomorphic Extension of Eigenfunctions

TL;DR

This paper proves a theorem that allows eigenfunctions of the Laplace-Beltrami operator on symmetric spaces of non-compact type to be extended holomorphically, using PDE techniques.

Contribution

It introduces a new holomorphic extension theorem for eigenfunctions on symmetric spaces, employing PDE methods.

Findings

Eigenfunctions extend holomorphically beyond their original domain

The extension is achieved through PDE techniques

The result applies to symmetric spaces of non-compact type

Abstract

Let X be a Riemannian symmetric space of non-compact type. We prove a theorem of holomorphic extension for eigenfunctions of the Laplace-Beltrami operator on X, by techniques from the theory of partial differential equations.