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SUMMARY:Non-local Schrödinger operators with eigenvalues at the spectral 
 edge - Giacomo Ascione (Università degli Studi di Napoli Federico II)
DTSTART:20220314T171500Z
DTEND:20220314T181500Z
UID:TALK170048@talks.cam.ac.uk
DESCRIPTION:A non-local Schr&ouml\;dinger operator arises as a sum of a no
 n-local operator (e.g.\, fractional Laplacian) and a multiplication operat
 or called potential. Such operators also have an interesting probabilistic
  connection\, relating with L&eacute\;vy-type/Feller processes whose featu
 res depend on the position in space\, and jumps of given size are encourag
 ed or suppressed in specific directions according to the values taken by t
 he potential. The spectral analysis of such operators is a challenging que
 stion\, relevant for both pure and applied purposes. Dependent on the prop
 erties of the potential\, the spectrum may or may not contain a discrete c
 omponent apart from the absolutely continuous part. In this talk we aim to
  describe what are the properties of potentials generating point spectrum 
 at the spectral edge\, i.e.\, an eigenvalue embedded at the bottom of the 
 continuous spectrum. This delicate borderline situation has several intere
 sting consequences and applications. This talk is based on joint work with
  Jozsef&nbsp\;L&ouml\;rinczi.
LOCATION:Seminar Room 2\, Newton Institute
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