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SUMMARY:On (global) unique continuation properties of the fractional discr
 ete Laplacian - Luz Roncal (BCAM - Basque Center for Applied Mathematics\,
  Universidad del País Vasco)
DTSTART:20220221T110000Z
DTEND:20220221T113000Z
UID:TALK167687@talks.cam.ac.uk
DESCRIPTION:We present various qualitative and quantitative (global) uniqu
 e continuation properties for the fractional discrete Laplacian. We show t
 hat while the fractional Laplacian enjoys striking rigidity properties in 
 the form of (global) unique continuation properties\, the fractional discr
 ete Laplacian does not enjoy these in general.\nWhile discretization thus 
 counteracts the strong rigidity properties of the continuum fractional Lap
 lacian\, by discussing quantitative forms of unique continuation\, we illu
 strate that these properties can be recovered if exponentially small (in t
 he lattice size) correction terms are added. This in particular allows us 
 to deduce stability properties for a discrete\, linear inverse problem for
  the fractional Laplacian.\nJoint work with Aingeru Fern&aacute\;ndez-Bert
 olin and Angkana R&uuml\;land.
LOCATION:Seminar Room 1\, Newton Institute
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