In t his talk I discuss a nonlocal inverse problem\, the fractional Calder&oacu te\;n problem. This is an inverse problem for a fractional Schrdinger equa tion in which one seeks to recover information on an unknown potential by exterior measurements. In the talk\, I prove uniqueness and stability of t he "\;infinite data problem"\;and then address the recovery questi on. This also yields (at firstsight) surprising insights on the uniqueness properties of the inverse problem in that it turns out that a single meas urement suffices to uniquely recover the potential.

These properties are based on the very strong unique continuation and approximation proper ties of fractional Schrdinger operators\, which are of independent interes t and which I also discuss in the talk.

This is based on joint work with T. Ghosh\, M. Salo and G. Uhlmann.

LOCATION:Big Seminar room Ground floor / Office Bldg West (I21.EG.101)\, IS T Austria ORGANIZER:msoronda@ist.ac.at SUMMARY:PDE Afternoon: Uniqueness\, stability and single measurement recove ry for the fractional Calderón problem URL:https://talks-calendar.app.ist.ac.at/events/1557 END:VEVENT END:VCALENDAR