Extracting Hadamard Coefficients from Green's Operators
Extracting Hadamard Coefficients from Green's Operators
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DissertationDate of Exam
27.01.2023Date of Publication
20.03.2023Advisor
Lesch, MatthiasCo-Referee
Strohmaier, AlexanderMetadata
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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.
Subjects
Lorentzian geometry, Hadamard expansion, wave equations, Green's operators, spectral action
Classification (DDC)
510 MathematikRonge, Lennart: Extracting Hadamard Coefficients from Green's Operators. - Bonn, 2023. - Dissertation, Rheinische Friedrich-Wilhelms-Universität Bonn.
Online-Ausgabe in bonndoc: https://nbn-resolving.org/urn:nbn:de:hbz:5-70229
Online-Ausgabe in bonndoc: https://nbn-resolving.org/urn:nbn:de:hbz:5-70229
@phdthesis{handle:20.500.11811/10718,
urn: https://nbn-resolving.org/urn:nbn:de:hbz:5-70229,
author = {{Lennart Ronge}},
title = {Extracting Hadamard Coefficients from Green's Operators},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2023,
month = mar,
note = {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.},
url = {https://hdl.handle.net/20.500.11811/10718}
}
urn: https://nbn-resolving.org/urn:nbn:de:hbz:5-70229,
author = {{Lennart Ronge}},
title = {Extracting Hadamard Coefficients from Green's Operators},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2023,
month = mar,
note = {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.},
url = {https://hdl.handle.net/20.500.11811/10718}
}
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