# Interpolation inequalities and spectral estimates for magnetic operators

## TL;DR

This paper develops new interpolation inequalities and spectral bounds for magnetic Schrödinger operators, providing explicit constants and validating their accuracy through numerical methods.

## Contribution

It introduces magnetic interpolation inequalities and spectral estimates with explicit bounds, advancing the analysis of magnetic Schrödinger operators.

## Key findings

- Derived explicit bounds for spectral estimates.
- Validated theoretical bounds with numerical methods.
- Enhanced understanding of magnetic operator inequalities.

## Abstract

We prove magnetic interpolation inequalities and Keller-Lieb-Thir-ring estimates for the principal eigenvalue of magnetic Schr{\"o}dinger operators. We establish explicit upper and lower bounds for the best constants and show by numerical methods that our theoretical estimates are accurate.