Rellich's theorem for spherically symmetric repulsive Hamiltonians

2017/03/28 by Kyohei Itakura, Itakura, Kyohei
Mathematics · #Advanced Operator Algebra Research #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Geometry and complex manifolds #Mathematical Physics (math-ph) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1703.09457

openalex publication_date 2017/03/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For spherically symmetric repulsive Hamiltonians we prove Rellich's theorem, or identify the largest weighted space of Agmon-Hörmander type where the generalized eigenfunctions are absent. The proof is intensively dependent on commutator arguments. Our novelty here is a use of conjugate operator associated with some radial flow, not with dilations and translations. Our method is simple and elementary, and does not employ any advanced tools such as the operational calculus or the Fourier analysis.

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