Fractional powers of the wave operator via Dirichlet-to-Neumann maps in anti-de Sitter spaces

TL;DR

This paper demonstrates that the fractional wave operator can be constructed as a Dirichlet-to-Neumann map for the Klein-Gordon equation in anti-de Sitter spaces, linking fractional PDEs with mathematical physics.

Contribution

It introduces a novel connection between fractional wave operators and Dirichlet-to-Neumann maps in anti-de Sitter spacetimes, expanding the mathematical framework of fractional PDEs.

Findings

Fractional wave operator expressed as Dirichlet-to-Neumann map.

Application to Klein-Gordon equation in anti-de Sitter spaces.

Discussion of generalizations of this relation.

Abstract

We show that the fractional wave operator, which is usually studied in the context of hypersingular integrals but had not yet appeared in mathematical physics, can be constructed as the Dirichlet-to-Neumann map associated with the Klein-Gordon equation in anti-de Sitter spacetimes. Several generalizations of this relation will be discussed too.