Resolvent Estimates for the 3D Schr\"odinger Operator with Inverse-Square Potential

TL;DR

This paper investigates resolvent estimates for the 3D Schrödinger operator with inverse-square potential, demonstrating improved bounds for non-radial functions by adapting Combes-Thomas estimates.

Contribution

It introduces adapted Combes-Thomas estimates for non-radial functions, revealing enhanced resolvent bounds similar to the Laplacian case.

Findings

Improved resolvent estimates for non-radial functions

Adaptation of Combes-Thomas estimates to inverse-square potential

Enhanced understanding of Schrödinger operator behavior

Abstract

We consider the unitary group for the Schr\"odinger operator with inverse-square potential. We adapt Combes-Thomas estimates to show that, when restricted to non-radial functions, the operator enjoys much better estimates that mirror those of the Laplacian.