Dispersion Estimates for Spherical Schr\"odinger Equations with Critical Angular Momentum

TL;DR

This paper establishes dispersion estimates for a specific class of radial Schrödinger operators with critical angular momentum, providing new insights into their spectral behavior and solution estimates.

Contribution

It introduces novel dispersion estimates for the critical angular momentum case and analyzes the Jost function near the spectrum edge.

Findings

Derived dispersion estimate for critical angular momentum case

Obtained new solution estimates for the differential equation

Analyzed the Jost function behavior at the spectrum edge

Abstract

We derive a dispersion estimate for one-dimensional perturbed radial Schr\"odinger operators where the angular momentum takes the critical value $l=-\frac{1}{2}$. We also derive several new estimates for solutions of the underlying differential equation and investigate the behavior of the Jost function near the edge of the continuous spectrum.