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DTSTART:20260329T030000
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DTSTAMP:20260425T092618Z
UID:6687bf08e3dea873408147@ist.ac.at
DTSTART:20251111T161500
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DESCRIPTION:Speaker: Steffen Polzer\nhosted by Robert Seiringer\nAbstract: 
 Wieners theorem connects the discrete part of a finite measure to the time
 -averaged squared modulus of its Fourier transform. It has a variety of ap
 plications\, for example\, in the proof of the famous RAGE theorem which c
 onnects the different spectral parts of a Hamiltonian H to the long-time b
 ehaviour of states under time evolution by the unitary group generated by 
 H.In order to study the bottom of the spectrum of the Hamiltonian\, it is 
 natural to shift the focus from the unitary group to the semigroup generat
 ed by H\, and hence to study the Laplace (rather than the Fourier) transfo
 rm of its spectral measures. This approach is particularly appealing in th
 e context of Feynman-Kac formulas\, which allow us to apply probabilistic 
 techniques to the study of semigroups.I will present two "Wiener-type" the
 orems that express the behaviour of a finite measure near the bottom of it
 s support in terms of time averaged quotients of its Laplace transform. Co
 nnecting these results to perturbation theory as well as to renewal theory
  yields natural interpretations both in functional analytic as well as in 
 probabilistic terms. As an application\, I will present criteria for the e
 xistence and non-existence of ground states of a finite-dimensional quantu
 m system coupled to a bosonic field.Based on joint work with Benjamin Hinr
 ichs
LOCATION:Office Bldg West / Ground floor / Heinzel Seminar Room (I21.EG.101
 )\, ISTA
ORGANIZER:boosthui@ist.ac.at
SUMMARY:Steffen Polzer: Wiener-type Theorems for the Laplace Transform
URL:https://talks-calendar.ista.ac.at/events/6105
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