Strichartz and Smoothing Estimates for Schroedinger Operators with Large Magnetic Potentials in R³

2006/08/28 by M. Burak Erdoğan, Michael Goldberg, Erdogan, M. Burak +3 · 1 citation
Mathematics · #35P25 #35Q40 #42B15 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.math/0608699

openalex publication_date 2006/08/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the time evolution of the operator H = -Δ+ i(A ⋅ ∇ + ∇ ⋅ A) + V in R³ satisfies Strichartz and smoothing estimates under suitable smoothness and decay assumptions on A and V but without any smallness assumptions. We require that zero energy is neither an eigenvalue nor a resonance.

Citations

• Spectral properties of Schrödinger operators and time-decay of the wave functions
• Time decay for solutions of Schr�dinger equations with rough and time-dependent potentials

Cited by

• Decay estimates for one Aharonov-Bohm solenoid in a uniform magnetic field III: Product cones

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