On the Limiting Absorption Principle for Schrödinger operators on waveguides

2019/02/06 by Alexandre Martin, Martin, Alexandre
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Analysis and Transform Methods #Mathematical Physics (math-ph) #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1902.02054

openalex publication_date 2019/02/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a Limiting Absorption Principle for Schrödinger 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 Schrödinger operators in singular waveguides.

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