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CATEGORIES:Geometric Analysis and Partial Differential Equati
ons seminar
SUMMARY:The Feynman propagator and its positivity properti
es - Andras Vasy (Stanford)
DTSTART;TZID=Europe/London:20170130T150000
DTEND;TZID=Europe/London:20170130T160000
UID:TALK67820AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/67820
DESCRIPTION:One usually considers wave equations as evolution
equations\, i.e. imposes initial data and solves t
hem. Equivalently\, one can consider the forward a
nd backward solution operators for the wave equati
on\; these solve an equation $Lu=f$\, for say $f$
compactly supported\, by demanding that $u$ is sup
ported at points which are reachable by forward\,
respectively backward\, time-like or light-like cu
rves. This property corresponds to causality. But
it has been known for a long time that in certain
settings\, such as Minkowski space\, there are oth
er ways of solving wave equations\, namely the Fey
nman and anti-Feynman solution operators (propagat
ors). I will explain a general setup in which all
of these propagators are inverses of the wave oper
ator on appropriate function spaces\, and also men
tion positivity properties\, and the connection to
spectral and scattering theory in Riemannian sett
ings\, as well as to the classical parametrix cons
truction of Duistermaat and Hormander.
LOCATION:CMS\, MR13
CONTACT:Prof. Mihalis Dafermos
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