A remark on the essential self-adjointness for Klein-Gordon type operators

TL;DR

This paper presents a simplified proof of the essential self-adjointness for Klein-Gordon type operators, building on prior work by Vasy and Nakamura-Taira, focusing on second order differential operators.

Contribution

The authors provide a more straightforward proof of essential self-adjointness for Klein-Gordon type operators, enhancing understanding and potentially simplifying future analyses.

Findings

Simplified proof of essential self-adjointness for Klein-Gordon operators

Focus on second order differential operators of real principal type

Builds on and clarifies previous proofs by Vasy and Nakamura-Taira

Abstract

Here we discuss a new simplified proof of the essential self-adjointness for formally self-adjoint differential operators of real principal type, previously proved by Vasy (2020) and Nakamura-Taira (2021). For simplicity, here we discuss the second order cases, i.e., Klein-Gordon type operators only.