Local form-subordination condition and Riesz basisness of root systems

Boris Mityagin, Petr Siegl*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We exploit the so-called form-local subordination in the analysis of non-symmetric perturbations of unbounded self-adjoint operators with isolated simple positive eigenvalues. If the appropriate condition relating the size of gaps between the unperturbed eigenvalues and the strength of perturbation, measured by the form-local subordination, is satisfied, the root system of the perturbed operator contains a Riesz basis and usual asymptotic formulas for perturbed eigenvalues and eigenvectors hold. The power of the abstract perturbation results is demonstrated particularly on Schrödinger operators with possibly unbounded or singular complex potential perturbations.

Original languageEnglish
Pages (from-to)83-119
Number of pages37
JournalJournal d'Analyse Mathematique
Issue number1
Publication statusPublished - 1 Oct 2019
Externally publishedYes

ASJC Scopus subject areas

  • Analysis
  • General Mathematics

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