2019/12/04 by Bony, Jean-Francois, Michel, Laurent, Ramond, Thierry
#35B34 #35J10 #35P25 #35S05 #47A10 #81Q20 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory (math.SP)
paper · doi:10.48550/arxiv.1912.02091
We prove that the results in scattering theory that involve resonances are still valid for non-analytic potentials, even if the notion of resonance is not defined in this setting. More precisely, we show that if the potential of a semiclassical Schrödinger operator is supposed to be smooth and to decrease at infinity, the usual formulas relating scattering quantities and resonances still hold. The main ingredient for the proofs is a resolvent estimate of a new type, relating the resolvent of an operator with the resolvent of its cut-off counterpart.