A Remark on the Essential Self-adjointness for Klein-Gordon-Type Operators

We discuss a new simplified proof of the essential self-adjointness for formally self-adjoint differential operators of real principal type with the null non-trapping condition, previously proved by Vasy (J Spectr Theory 10: 439-461, 2020) and Nakamura-Taira (Ann Henri Lebesgue 4: 1035-1059, 2021). For simplicity, here we discuss the second-order cases, i.e., Klein-Gordon-type operators only.

Automated summary

We present a simplified proof of the essential self-adjointness for formally self-adjoint differential operators of real principal type with the null non-trapping condition, which was previously proved by Vasy (J Spectr Theory 10: 439-461, 2020) and Nakamura-Taira (Ann Henri Lebesgue 4: 1035-1059, 2021). We focus on second-order cases, specifically Klein-Gordon-type operators.