Local form-subordination condition and Riesz basisness of root systems

Boris Mityagin, Petr Siegl

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Abstract

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 sizeof 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 Schrodinger operators with possibly unbounded or singular complex potential perturbations.
Original languageEnglish
Number of pages29
JournalJournal d'Analyse Mathématique
Early online date09 Oct 2019
DOIs
Publication statusEarly online date - 09 Oct 2019

Bibliographical note

arxiv:1608.00224

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