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SUMMARY:Random acoustic boundary conditions and Weyl's law [Event canceled
 ]
DTSTART:20250123T131500Z
DTEND:20250123T150000Z
DTSTAMP:20260420T153800Z
UID:indico-event-179@math-events.uni-bonn.de
CONTACT:kappes@iam.uni-bonn.de
DESCRIPTION:Speakers: Illia Karabash (IAM Funktionalanalysis)\n\nMotivated
  by engineering and Photonics research on  resonators in random or uncert
 ain environments\, we introduce rigorous randomizations of boundary condit
 ions for acoustic wave equations in Lipschitz domains. First\, a parametri
 zation of essentially all m-dissipative boundary conditions in the boundar
 y L2-space is constructed with the use of boundary tuples. Randomizations 
 of these boundary conditions lead to acoustic operators random in the reso
 lvent sense. We prove this using Neumann-to-Dirichlet maps and generalized
  Krein resolvent formulae. In order to pass to point processes of random 
 eigenvalues\, we give a description of  random m-dissipative boundary con
 ditions that produce acoustic operators with almost surely (a.s.) compact 
 resolvents\, and so\, also with a.s. discrete spectra. Based on these resu
 lts\, examples of mathematically convenient randomizations are constructed
  in terms of eigenfunctions of the Laplace-Beltrami operator on the bounda
 ry. We show that for these special randomizations the resolvent compactnes
 s is connected with the  Weyl law for the Laplace-Beltrami eigenvalues\, 
 and also discuss available Weyl-asymptotic results for the case of  nonsm
 ooth boundaries. \n\nhttps://math-events.uni-bonn.de/event/179/
LOCATION:Endenicher Allee 60/1-016 - Lipschitzsaal (Mathezentrum)
URL:https://math-events.uni-bonn.de/event/179/
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