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\noindent{\bf Mathematisches Oberseminar} {\it PDG und
Spektraltheorie} (SoSe 2015).

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\noindent{\bf Date:} 18.06.2015.

\noindent{\bf Time and place:} 14:15 in B 134.

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\noindent{\bf Speaker:} Rafael Tiedra (Pontifical Catholic University of Chile).

\noindent{\bf Titel:} {\it Commutator criteria for strong mixing.}


\noindent{\bf Abstract:}

\noindent We present new criteria, based on commutator methods, for
the strong mixing property of discrete flows $\{U_N\}$ and continuous
flows $\{e^{-itH}\}$ induced by unitary operators $U$ and self-adjoint
operators $H$ in a Hilbert space $\mathfrak{H}$. Our approach put into evidence a
general definition for the topological degree of the maps $N\mapsto U^N$ and
$t\mapsto e^{-itH}$ with values in the unitary group of $\mathfrak{H}$. Among other
examples, our results apply to skew products of compact Lie groups,
time changes of horocycle flows and adjacency operators on graphs. \\


 


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Thomas {\O}stergaard S{\o}rensen

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