Schrödinger Dispersive Estimates for a Scaling-Critical Class of Potentials

2010/09/27 by Marius Beceanu, Michael Goldberg · 50 citations
Mathematics · #Advanced Mathematical Physics Problems #Class (philosophy) #Closure (psychology) #Complex system #Eigenfunction #Interval (graph theory) #Mathematical Analysis and Transform Methods #Nonlinear system #Pseudodifferential operators #Spectral Theory in Mathematical Physics #math.AP

paper · pdf · doi:10.1007/s00220-012-1435-x

published in Communications in Mathematical Physics 314(2), 471-481 (Springer Science+Business Media) · 10 pages

arxiv created 2010/09/27 · openalex publication_date 2012/02/07 · openalex created_date 2016/06/24 · arxiv updated 2016/08/31 · openalex updated_date 2026/08/05

Abstract

We prove a dispersive estimate for the evolution of Schroedinger operators H = -Δ+ V(x) in three dimensions. The potential should belong to the closure of bounded compactly-supported functions with respect to the golbal Kato norm. Some additional spectral conditions are imposed, namely that no resonances or eigenfunctions of H exist anywhere on the positive half-line. The proof is an application of a new version of Wiener's L¹ inversion theorem.

Citations

• Time decay for solutions of Schr�dinger equations with rough and time-dependent potentials
• Decay estimates for Schrödinger operators
• Dispersive Estimates for Schr�dinger Operators in Dimensions One and Three
• Schrödinger semigroups