One-dimensional perturbations of unbounded selfadjoint operators with empty spectrum

2013/04/21 by Anton Baranov, Anton D. Baranov, Baranov, Anton D. +2
Mathematics · #47A55 #47B07 #47B25 #Complex Variables (math.CV) #Differential Equations and Boundary Problems #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #math.CV #math.FA #math.SP #msc:47A55 #msc:47B07 #msc:47B25

paper · pdf · doi:10.48550/arxiv.1304.5800

20 pages. Part of these results was announced in arXiv:1212.6014

arxiv created 2013/04/21 · openalex publication_date 2013/04/21 · arxiv updated 2013/04/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study spectral properties of one-dimensional singular perturbations of an unbounded selfadjoint operator and give criteria for the possibility to remove the whole spectrum by a perturbation of this type. A counterpart of our results for the case of bounded operators provides a complete description of compact selfadjoint operators whose rank one perturbation is a Volterra operator.

Citations

• Recent developments in spectral synthesis for exponential systems and\n for non-self-adjoint operators

Related

• Completeness and spectral synthesis of nonselfadjoint one-dimensional\n perturbations of selfadjoint operators
• Direct and inverse spectral problems for rank-one perturbations of\n self-adjoint operators
• Spectral perturbation bounds for selfadjoint operators
• On non-selfadjoint operators with finite discrete spectrum
• Non-symmetric perturbations of self-adjoint operators