Wave operator bounds for 1-dimensional Schrödinger operators with singular potentials and applications

Abstract

Boundedness of wave operators for Schrödinger operators in one space dimension for a class of singular potentials, admitting finitely many Dirac delta distributions, is proved. Applications are presented to, for example, dispersive estimates and commutator bounds.

16 pages, 0 figures

References in corpus (4)

• Fast soliton scattering by delta impurities
• Soliton splitting by external delta potentials
• Scattering, homogenization and interface effects for oscillatory potentials with strong singularities
• Long time dynamics near the symmetry breaking bifurcation for nonlinear Schrödinger/Gross-Pitaevskii Equations

Cited by in corpus (6)

• Two dimensional Schr{\" o}dinger operators with point interactions: threshold expansions, zero modes and $L^p$-boundedness of wave operators
• Quantum backflow and scattering
• The $L^p$ boundedness of wave operators for the three-dimensional multi-centre point interaction
• Dispersion for the Schrödinger equation on the line with multiple Dirac delta potentials and on delta trees
• Scattering, homogenization and interface effects for oscillatory potentials with strong singularities
• Stability of small solitary waves for the 1$d$ NLS with an attractive delta potential