In this article, we prove that the completeness of the Hamilton flow and
essential self-dajointness are equivalent for real principal type operators on
the circle. Moreover, we study spectral properties of these operators.Comment: 21 page

Taira, Kouichi

English

arXiv

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 page

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

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