Extracting Hadamard Coefficients from Green's Operators
Differential Geometry
2023-09-29 v3 Analysis of PDEs
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.
Cite
@article{arxiv.2303.09976,
title = {Extracting Hadamard Coefficients from Green's Operators},
author = {Lennart Ronge},
journal= {arXiv preprint arXiv:2303.09976},
year = {2023}
}
Comments
This is the Author's Ph. D. thesis (with minor typo corrections), advised by Prof. Matthias Lesch and unofficially also advised by Dr. Koen van den Dungen. A shorter and more easily readable version of the part on additional expansions is in the making