Local time decay for fractional Schrödinger operators with slowly decaying potentials and a weaker Agmon type estimate in a classically forbidden region
Abstract
A local time decay estimate of fractional Schrödinger operators with slowly decaying positive potentials are studied. It is shown that its resolvent is smooth near zero and the time propagator has fast local time decay which is very different from very shortrange cases. The key element of the proof is to establish a weaker Agmon estimate for a classically forbidden region using exotic symbol calculus. As a byproduct, we prove that the Riesz operator is a pseudodifferential operator with an exotic symbol.
 Publication:

arXiv eprints
 Pub Date:
 March 2024
 DOI:
 10.48550/arXiv.2403.16148
 arXiv:
 arXiv:2403.16148
 Bibcode:
 2024arXiv240316148T
 Keywords:

 Mathematics  Analysis of PDEs;
 Mathematical Physics;
 Mathematics  Spectral Theory;
 35P25;
 35Q41;
 47A40;
 47G30
 EPrint:
 34pages