A parametrix for the fundamental solution of the Klein-Gordon equation on asymptotically de Sitter spaces

2009/05/04 by Dean Baskin, Baskin, Dean
Computer Science · Mathematics · #35L05 (Prmary) #35Q75 #58J45 #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #advanced mathematical theories #math.AP #math.DG #msc:35L05 #msc:35Q75 #msc:58J45

paper · pdf · doi:10.48550/arxiv.0905.0447

42 pages; v2: minor revisions reflecting referee comments

openalex publication_date 2009/05/04 · arxiv created 2010/05/31 · arxiv updated 2010/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we construct a parametrix for the forward fundamental solution of the wave and Klein-Gordon equations on asymptotically de Sitter spaces without caustics. We use this parametrix to obtain asymptotic expansions for solutions of the inhomogeneous equation and to obtain a uniform L^p estimate for a family of bump functions traveling to infinity.

Related

• The Klein-Gordon equation on asymptotically Minkowski spacetimes: causal propagators
• The wave equation on asymptotically de Sitter-like spaces
• The wave equation on asymptotically Anti-de Sitter spaces
• Asymptotics and Scattering for Wave-Klein-Gordon Systems
• Strichartz estimates on asymptotically de Sitter spaces