# The $L^p$ boundedness of wave operators for the three-dimensional multi-centre point interaction

## TL;DR

This paper establishes the $L^p$ boundedness of wave operators for 3D Schrödinger operators with multi-centre point interactions, showing boundedness for $1<p<3$ and unboundedness outside this range.

## Contribution

It provides a comprehensive analysis of $L^p$ boundedness for wave operators in multi-centre point interaction models, extending understanding to arbitrary centres and strengths.

## Key findings

- Wave operators are bounded in $L^p$ for $1<p<3$.
- Wave operators are unbounded outside the $p$ range.
- Results hold for arbitrary centres and strengths.

## Abstract

We prove that, for arbitrary centres and strengths, the wave operators for three dimensional Schr\"odinger operators with multi-centre local point interactions are bounded in $L^p(\mathbb{R}^3)$ for $1<p<3$ and unbounded otherwise.