Wave operator bounds for 1-dimensional Schr\"odinger operators with singular potentials and applications

TL;DR

This paper proves the boundedness of wave operators for 1D Schrödinger operators with singular potentials, including finitely many Dirac deltas, and explores applications like dispersive estimates and commutator bounds.

Contribution

It establishes boundedness results for wave operators with singular potentials and demonstrates their applications in dispersive and commutator estimates.

Findings

Wave operators are bounded for Schrödinger operators with finitely many Dirac delta potentials.

Applications include improved dispersive estimates.

Results extend understanding of singular potential effects on wave propagation.

Abstract

Boundedness of wave operators for Schr\"odinger 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.