LIPSCHITZ STABILITY FOR THE FINITE DIMENSIONAL FRACTIONAL CALDERON PROBLEM WITH FINITE CAUCHY DATA

In this note we discuss the conditional stability issue for the finite dimensional Calderon problem for the fractional Schrodinger equation with a finite number of measurements. More precisely, we assume that the unknown potential q is an element of L-infinity (Omega) in the equation ((-Delta)(s) + q)u = 0 in Omega subset of R-n satisfies the a priori assumption that it is contained in a finite dimensional subspace of L-infinity (Omega). Under this condition we prove Lipschitz stability estimates for the fractional Calderon problem by means of finitely many Cauchy data depending on q. We allow for the possibility of zero being a Dirichlet eigenvalue of the associated fractional Schrodinger equation. Our result relies on the strong Runge approximation property of the fractional Schrodinger equation.