Extracting Hadamard Coefficients from Green's Operators

2023/03/17 by Lennart Ronge, Ronge, Lennart
Mathematics · Physics and Astronomy · #53B30 #58B34 (Secondary) #58J45 (Primary) 58K55 #Advanced Differential Geometry Research #Advanced Topics in Algebra #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.2303.09976

openalex publication_date 2023/03/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We develop a formula for the diagonal values of the Hadamard coefficients associated to a normally hyperbolic operator on a globally hyperbolic spacetime in terms of the advanced and retarded Green's operators. We develop a local formula as well as formulae for integrals over (parts of) the diagonal. Furthermore, we develop analogues of the Hadamard expansion for powers of the advanced/retarded Green's operators and an analogue of a resolvent.

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