Virtual levels, virtual states, and the limiting absorption principle for higher order differential operators in 1D

2024/12/30 by Andrew Comech, Comech, Andrew, Hatice Pekmez +1
Mathematics · Engineering · #Spectral Theory in Mathematical Physics #Gas Dynamics and Kinetic Theory #Electromagnetic Simulation and Numerical Methods

paper · pdf · doi:10.48550/arxiv.2412.20712

Abstract

We consider the resolvent estimates and properties of virtual states of the higher order derivatives in one dimension, focusing on Schroedinger-type operators of degree N=3 (the approach applies to higher orders). The derivation is based on the construction of the Jost solution for higher order differential operators and on restricting the resolvent onto subspaces of finite codimension.

Related

• Virtual levels and virtual states of linear operators in Banach spaces.\n Applications to Schroedinger operators
• Limiting absorption principle and virtual levels of operators in Banach\n spaces
• A Limiting absorption principle for high-order Schrödinger operators in critical spaces
• Dispersive estimates for higher order Schrödinger operators with scaling-critical potentials
• On the limiting absorption principle for a new class of schroedinger hamiltonians