TL;DR
This paper proves local decay estimates for Schrödinger equations using asymptotic completeness, extending to time-dependent potentials and deriving global Strichartz estimates without relying on resolvent methods.
Contribution
It introduces a novel proof technique for local decay estimates based on asymptotic completeness, applicable to time-dependent potentials.
Findings
Local decay estimates established for Schrödinger equations.
Extension to time-dependent potentials without resolvent estimates.
Global Strichartz estimates derived for quasi-periodic potentials.
Abstract
We give a proof of Local Decay Estimates for Schr\"odinger type equations, which is based on the knowledge of Asymptotic Completeness (AC). This approach extends to time dependent potential perturbations, as it does not rely on Resolvent Estimates or related methods. Global in time Strichartz estimates follow for quasi-periodic time-dependent potentials from our results.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsNumerical methods in inverse problems · Spectral Theory in Mathematical Physics · Advanced Mathematical Physics Problems