On the limiting absorption principle for a new class of schroedinger hamiltonians

TL;DR

This paper establishes the limiting absorption principle for a broad class of Schrödinger Hamiltonians, including short and long-range potentials, ensuring better understanding of their spectral and resolvent properties.

Contribution

It introduces a new class of Schrödinger Hamiltonians for which the limiting absorption principle is proven, covering both short and long-range potentials with optimal behavior at infinity.

Findings

Proved the limiting absorption principle for the new class of Hamiltonians.

Analyzed the continuity properties of the resolvent boundary values.

Extended the principle to potentials with optimal decay at infinity.

Abstract

We prove the limiting absorption principle and discuss the continuity properties of the boundary values of the resolvent for a class of form bounded perturbations of the Euclidean Laplacian $\Delta$ that covers both short and long range potentials with an essentially optimal behaviour at infinity.