The Birman--Solomyak theorem revisited: a novel elementary proof, generalisation, and applications

TL;DR

This paper presents a new, concise proof of the Birman--Solomyak theorem for Hilbert--Schmidt operators, extends its scope, and demonstrates its application to a Schrödinger--Poisson system.

Contribution

It offers a novel, elementary proof of the theorem, generalizes its results, and applies it to a specific quantum-mechanical system.

Findings

New elementary proof of Birman--Solomyak theorem

Generalization of the theorem's scope

Application to Schrödinger--Poisson system

Abstract

We provide a new short proof for the Birman--Solomyak theorem for Hilbert--Schmidt operators and give an application to a Schr\"odinger--Poisson system.