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

Kouichi Taira

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

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2004.07547 v4 pith:MB3H4UOZ submitted 2020-04-16 math.AP math-phmath.MP

Kouichi Taira This is my paper · ORCID

classification math.APmath-phmath.MP

keywords operatorscirclecompletenessessentialmoreoverprincipalrealscattering

verification ladder T0 review T1 audit T2 compute T3 formal

0 comments

read the original 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.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Dirac operators and local invariants on perturbations of Minkowski space
math.AP 2024-12 conditional novelty 7.0 of 10

The squared Lorentzian Dirac operator on small Minkowski perturbations has real spectrum plus isolated resonances, and a zeta-function residue equals the scalar curvature plus twisting curvature.

Pith tools