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SUMMARY:The Feynman propagator and its positivity properties - Andras Vasy
  (Stanford)
DTSTART:20170130T150000Z
DTEND:20170130T160000Z
UID:TALK67820@talks.cam.ac.uk
CONTACT:Prof. Mihalis Dafermos
DESCRIPTION:One usually considers wave equations as evolution equations\, 
 i.e. imposes initial data and solves them. Equivalently\, one can consider
  the forward and backward solution operators for the wave equation\; these
  solve an equation $Lu=f$\, for say $f$ compactly supported\, by demanding
  that $u$ is supported at points which are reachable by forward\, respecti
 vely backward\, time-like or light-like curves. This property corresponds 
 to causality. But it has been known for a long time that in certain settin
 gs\, such as Minkowski space\, there are other ways of solving wave equati
 ons\, namely the Feynman and anti-Feynman solution operators (propagators)
 . I will explain a general setup in which all of these propagators are inv
 erses of the wave operator on appropriate function spaces\, and also menti
 on positivity properties\, and the connection to spectral and scattering t
 heory in Riemannian settings\, as well as to the classical parametrix cons
 truction of Duistermaat and Hormander.
LOCATION:CMS\, MR13
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