# On the Limiting Absorption Principle for Schr{\"o}dinger operators on waveguides

## TL;DR

This paper establishes a Limiting Absorption Principle for Schrödinger operators on waveguides with various boundary conditions, using Mourre theory with novel conjugate operators, advancing understanding of spectral properties in singular geometries.

## Contribution

It introduces a new approach employing Mourre theory with alternative conjugate operators to prove the principle in complex waveguide geometries.

## Key findings

- Proves Limiting Absorption Principle for Schrödinger operators in waveguides.
- Extends spectral analysis techniques to singular waveguides.
- Uses Mourre theory with non-standard conjugate operators.

## Abstract

We prove a Limiting Absorption Principle for Schr{\"o}dinger operators in tubes about infinite curves embedded in the Euclidian space with different types of boundary conditions. The argument is based on the Mourre theory with conjugate operators different from the generator of dilations which is usually used in this case, and permits to prove a Limiting Absorption Principle for Schr{\"o}dinger operators in singular waveguides.