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SUMMARY:$L_1$-Estimates for Eigenfunctions of the Dirichlet Laplacian - He
 mpel\, R (Technische Universitt Braunschweig)
DTSTART:20150624T140000Z
DTEND:20150624T150000Z
UID:TALK59929@talks.cam.ac.uk
CONTACT:42080
DESCRIPTION:Co-authors: Michiel van den Berg (U Bristol)\, J"urgen Voigt (
 TU Dresden) \n\nFor $d in {f N}$ and  $Omega \ne mptyset$ an open set in
 \n ${f R}^d$\, we consider the eigenfunctions $Phi$ of the Dirichlet\n La
 placian $-Delta_Omega$ of $Omega$. We do {it not} require \n $Omega$ to be
  of finite volume. \n %\n If $Phi$ is associated with an\n eigenvalue belo
 w the essential spectrum of $-Delta_Omega$\, we\n provide estimates for th
 e $L_1$-norm of $Phi$\n in terms of the $L_2$-norm of $Phi$ and suitable s
 pectral data of $-Delta_Omega$. \n The main idea in obtaining such estimat
 es consists in finding a---sufficiently \n small---subset $Omega'  ubset O
 mega$ where $Phi$ is localized in the sense that \n $Phi$ decays exponenti
 ally as one moves away from $Omega'$.  \n\n These $L_1$-estimates are then
  used in the comparison of the\n heat content of $Omega$ at time $t>0$ and
 \n the heat trace at times $t' > 0$\, where a two-sided estimate is establ
 ished.\n \nskip.5em \n\nThis is joint work with Michiel van den Berg (Bri
 stol) and J"urgen Voigt (Dresden)\, with \nimprovements by Hendrik Vogt (D
 resden). \n
LOCATION:Seminar Room 1\, Newton Institute
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