Equivalence of classical and quantum completeness for real principal type operators on the circle
Year: 2025
Type: article
Abstract: In this article, we prove that the completeness of the Hamilton flow and essential self-adjointness are equivalent for real principal type operators on the circle. Moreover, we study spectral properties of these operators. The proof is based on the construction of eigenfunctions with non-real eigenvalues which is well-known in scattering theory. Moreover, the relationship between scattering theory and the essential self-adjointness is explained.
DOI: 10.1090/tran/9599
Author: Kouichi Taira
Institution: Kyushu University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7115679190