Dispersive estimates for Schroedinger operators in the presence of a resonance and/or an eigenvalue at zero energy in dimension three: II

2005/04/28 by Mehmet Burak Erdogan, Wilhelm Schlag, Erdogan, Mehmet Burak +1 · 2 citations
Mathematics · Physics and Astronomy · #35P05 #35Q55 #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory in Mathematical Physics #math-ph #math.AP #math.MP #msc:35P05 #msc:35Q55

paper · pdf · doi:10.48550/arxiv.math/0504585

1 figure; this is the final version of our paper. Some minor changes have been made

openalex publication_date 2005/04/28 · arxiv created 2006/01/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider non-selfadjoint operators of the kind arising in linearized NLS and prove dispersive bounds for the time-evolution without assuming that the edges of the essential spectrum are regular. Our approach does not depend on any specific properties of NLS. Rather, it is axiomatic on the linear level, and our results are obtained from four assumptions (which are of course motivated by NLS). This work is in three dimensions.

Citations

• Spectral properties of Schrödinger operators and time-decay of the wave functions
• Asymptotic stability of N-soliton states of NLS
• Uniqueness of positive solutions of Δu−u+up=0 in Rn
• Time decay for solutions of Schr�dinger equations with rough and time-dependent potentials
• Existence of solitary waves in higher dimensions

Cited by

• A Critical Centre-Stable Manifold for the Cubic Focusing Schroedinger Equation in Three Dimensions
• A Centre-Stable Manifold for the Focussing Cubic NLS in ℝ¹⁺³

Related

• Dispersive estimates for Schrödinger operators in the presence of a resonance and/or an eigenvalue at zero energy in dimension three: I
• A dispersive bound for three-dimensional Schroedinger operators with zero energy eigenvalues
• Dispersive estimates for Schroedinger operators: A survey
• Dispersive estimates for inhomogeneous fourth-order Schrödinger operator in 3D with zero energy obstructions
• Dispersive estimates for 1D matrix Schrödinger operators with threshold resonance