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UID:7618@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20170306T100000
DTEND;TZID=Europe/Paris:20170306T110000
DTSTAMP:20241120T204427Z
URL:https://www.i2m.univ-amu.fr/evenements/001-improvement-of-liouville-pr
 operty-for-discrete-harmonic-functions/
SUMMARY:Alexander Logunov (Saint Petersburg Univ and Tel Aviv University): 
 0\,01% improvement of Liouville property for discrete harmonic functions
DESCRIPTION:Alexander Logunov: Let u be a harmonic function on the plane. T
 he Liouville theorem claims that if |u| is bounded on the whole plane\, th
 en u is identically constant. At the same moment for any angle on the plan
 e R^2\, there exist a harmonic function that is non-constant and is bounde
 d outside the angle. It appears that if u is a harmonic function on a latt
 ice Z^2\, and |u| &lt\; 1 on 99\,99% of Z^2\, then u is a constant functio
 n. In particular there are no (non-constant) discrete harmonic functions b
 ounded outside a sufficiently small angle. Based on a joint work (in progr
 ess) with L. Buhovsky\, Eu. Malinnikova and M. Sodin.\n\n\n\nhttps://arxiv
 .org/abs/1712.07902\n\n\n\n
ATTACH;FMTTYPE=image/jpeg:https://www.i2m.univ-amu.fr/wp-content/uploads/2
 020/01/Alexander_Logunov.jpg
CATEGORIES:Séminaire,Analyse et Géométrie
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