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SUMMARY:Jeremy Faupin (Lorraine)
DTSTART:20241217T131500Z
DTEND:20241217T140000Z
DTSTAMP:20260423T052712Z
UID:MAS-MP/86
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MAS-MP/86/">
 On the number of bound states for the fractional Schrödinger operator wit
 h a super-critical exponent</a>\nby Jeremy Faupin (Lorraine) as part of Mu
 nich-Copenhagen-Santiago Mathematical Physics seminar\n\n\nAbstract\nWe wi
 ll consider in this talk the number of negative eigenvalues $N_{<0}(H_s)$ 
 of the fractional Schrödinger operator $H_s=(-\\Delta)^s-V(x)$ in $L^2(\\
 mathbb{R}^d)$\, in any dimension $d\\ge 1$ and for any $s>0$. After recall
 ing results in the subcritical case $d/2>s$\, including the celebrated Cwi
 kel-Lieb-Rozenblum bounds for dimensions $d\\ge3$ and Bargmann’s estimat
 e in dimension $d=1$\, we will focus on the supercritical case $s\\ge d/2$
 . We will describe bounds on $N_{<0}(H_s)$ depending on $s-d/2$ being an i
 nteger or not\, the critical case $s=d/2$ requiring a further analysis. Th
 is is joint work with Sébastien Breteaux and Viviana Grasselli.\n
LOCATION:https://researchseminars.org/talk/MAS-MP/86/
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