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DTSTAMP:20260904T132120Z
DESCRIPTION:Reverse Agmon estimates for Schr\'{o}dinger eigenfunctions\n\nL
 et $(M\,g)$ be a compact\, Riemannian manifold and $V in C^{infty}(M\; R)$
 . Given a regular energy level $E > min V$\, we consider $L^2$-normalized 
 eigenfunctions\, $u_h\,$ of the Schrodinger operator $P(h) = - h^2 Delta_g
  + V - E(h)$ with $P(h) u_h = 0$ and $E(h) = E + o(1)$ as $h o 0^+.$ The w
 ell-known Agmon-Lithner estimates cite{Hel} are exponential decay estimate
 s (ie. upper bounds) for eigenfunctions in the forbidden region ${ V>E }.$
  The decay rate is given in terms of the Agmon distance function $d_E$ ass
 ociated with the degenerate Agmon metric $(V-E)_+ \, g$ with support in th
 e forbidden region. Our main result is a partial converse to the Agmon est
 imates (ie. exponential {em lower} bounds for the eigenfunctions) in terms
  of Agmon distance in the forbidden region under a control assumption on e
 igenfunction mass in the allowable region ${ V< E }$ arbitrarily close to 
 the caustic $ { V = E }.$ I will explain this result in my talk and then g
 ive some applications to hypersurface restriction bounds for eigenfunction
 s in the forbidden region along with corresponding nodal intersection esti
 mates. This is joint work with Xianchao Wu.\n
DTSTART:20181123T190000Z
DTEND:20181123T200000Z
LOCATION:Room VCH-2810\, CA\, Université Laval
SUMMARY:John Toth (McGill University)
URL:https://www.mcgill.ca/mathstat/channels/event/john-toth-mcgill-universi
 ty-291804
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