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UID:c887faaefd6c96bd1085d3677bf58699
CATEGORIES:Joint Princeton-Rutgers Seminar on Geometric PDE's
CREATED:20240310T184513
SUMMARY: Fastest rate of localization for eigenfunctions
LOCATION:Room 208\, Science & Engineering Resource Center (SEC 208)\, Busch Camp
 us\, Rutgers University
DESCRIPTION:The Laplace operator in the Euclidean space has no L^2 eigenfunctions, but 
 by perturbing the metric or adding a potential one can construct a plenty o
 f examples of operators with L^2 integrable eigenfunctions. Landis conjectu
 re states that any non-zero solution to Delta u + V u=0 in the Euclidean sp
 ace with real bounded V cannot decay faster than exponentially near infinit
 y. If we are allowed to slightly perturb the coefficients of the Laplace op
 erator (for instance taking a small smooth perturbation of the Euclidean me
 tric and taking the Laplace operator for this metric ) how fast can we forc
 e an eigenfunction of the perturbed Laplace operator to be localized? We wi
 ll review known results, related open questions and recent constructions of
  Nazarov and AL, Filonov and Krymskii, Pagano, AL and Krymskii of eigenfunc
 tions to linear elliptic operators with smooth coefficients, which are loca
 lized much faster than exponentially.\n
X-ALT-DESC;FMTTYPE=text/html:<p>The Laplace operator in the Euclidean space has no L^2 eigenfunctions, b
 ut by perturbing the metric or adding a potential one can construct a plent
 y of examples of operators with L^2 integrable eigenfunctions. Landis conje
 cture states that any non-zero solution to Delta u + V u=0 in the Euclidean
  space with real bounded V cannot decay faster than exponentially near infi
 nity. If we are allowed to slightly perturb the coefficients of the Laplace
  operator (for instance taking a small smooth perturbation of the Euclidean
  metric and taking the Laplace operator for this metric ) how fast can we f
 orce an eigenfunction of the perturbed Laplace operator to be localized? We
  will review known results, related open questions and recent constructions
  of Nazarov and AL, Filonov and Krymskii, Pagano, AL and Krymskii of eigenf
 unctions to linear elliptic operators with smooth coefficients, which are l
 ocalized much faster than exponentially.</p>
CONTACT:Aleksandr Logunov, MIT
DTSTAMP:20260830T215526
DTSTART;TZID=America/New_York:20240329T140000
DTEND;TZID=America/New_York:20240329T150000
SEQUENCE:0
TRANSP:OPAQUE
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