The structure of the wave operators in four dimensions in the presence of resonances

2023/11/28 by Alexander, Angus, Rennie, Adam
#35P25 #81U05 #FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2311.16438

Abstract

We show that the wave operators for Schrödinger scattering in ℝ⁴ have a particular form which depends on the existence of resonances. As a consequence of this form, we determine the contribution of resonances to the index of the wave operator.

Related

• Explicit formulas for the Schroedinger wave operators in R²
• The L^p-boundedness of wave operators for fourth order Schrödinger operators on \mathbb R⁴
• The L^p-boundedness of wave operators for four dimensional Schrödinger operators with threshold resonances
• Spectral and scattering theory of fourth order differential operators
• Mathematical Study of Scattering Resonances