Equivalence of classical and quantum completeness for real principal type operators on the circle

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.

Significant revisions were made. 29 pages

References in corpus (6)

• Microlocal analysis of forced waves
• Scattering theory for the Schrodinger equation with repulsive potential
• Essential self-adjointness of real principal type operators
• The scattering matrix for 0th order pseudodifferential operators
• 0-th Order Pseudo-differential Operator on the Circle
• Scattering theory for repulsive Schrödinger operators and applications to limit circle problem

Cited by in corpus (1)

• Complex powers of the wave operator and the spectral action on Lorentzian scattering spaces