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Semiclassical estimates for non selfadjoint operators with double characteristics

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24 pages
Semiclassical estimates for non-selfadjoint operators with double characteristics Michael Hitrik Department of Mathematics, University of California, Los Angeles Joint work with Karel Pravda-Starov M. Hitrik (UCLA) 1 / 24

  • boutet de monvel

  • canonical symplectic

  • imf

  • semigroup properties

  • selfadjoint operators

  • semiclassical estimates

  • hamilton map

  • recent works

  • kramers–fokker–planck operator


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Semiclassical estimates for non-selfadjoint operators with double characteristics
M.Hitrik
Michael Hitrik
Department of Mathematics, University of California, Los Angeles
(UCLA)
Joint work with Karel Pravda-Starov
1/42
Introduction
The study of operators with double characteristics has a long tradition in theanalysisoflinearPDE.BoutetdeMonvel,Grigis,Heler,Ho¨rmander, Ivrii,Petkov,Sj¨ostrand...(classicalworksonhypoellipticityfromthe 1970’s).
Recent works on Kramers–Fokker–Planck type operators have brought aboutarenewedinterestinthissubject.H´erauNier,HelerNier, He´rauSjo¨strandStolk(20042006).
In a recent work with K. Pravda–Starov we have investigated spectral and semigroup properties for a class ofnon-selfadjointquadratic operators that are alsonon-elliptic.
M.Hirtik(UCLA)2/24