@article{13ce5159083f4b9680f70110976d69a5,
title = "Local form-subordination condition and Riesz basisness of root systems",
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 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 Schr{\"o}dinger operators with possibly unbounded or singular complex potential perturbations.",
author = "Boris Mityagin and Petr Siegl",
note = "Funding Information: 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 Schr{\"o}dinger operators with possibly unbounded or singular complex potential perturbations. publisher-imprint-name Hebrew University Magnes Press article-contains-esm No article-numbering-style Unnumbered article-registration-date-year 2019 article-registration-date-month 10 article-registration-date-day 8 article-toc-levels 0 journal-product ArchiveJournal numbering-style Unnumbered article-grants-type Regular metadata-grant OpenAccess abstract-grant OpenAccess bodypdf-grant Restricted bodyhtml-grant Restricted bibliography-grant Restricted esm-grant OpenAccess online-first true pdf-file-reference BodyRef/PDF/11854_2019_Article_53.pdf target-type OnlinePDF article-type OriginalPaper journal-subject-primary Mathematics journal-subject-secondary Analysis journal-subject-secondary Functional Analysis journal-subject-secondary Dynamical Systems and Ergodic Theory journal-subject-secondary Abstract Harmonic Analysis journal-subject-secondary Partial Differential Equations journal-subject-collection Mathematics and Statistics open-access false We acknowledge the support of the University of Bern (B.M., October–November 2015) and the Ohio State University (P.S., May 2016) for our visits there. The research of P.S. is supported by the Swiss National Science Foundation Ambizione grant No. PZ00P2 154786. Publisher Copyright: {\textcopyright} 2019, The Hebrew University of Jerusalem.",
year = "2019",
month = oct,
day = "1",
doi = "10.1007/s11854-019-0053-3",
language = "English",
volume = "139",
pages = "83--119",
journal = "Journal d'Analyse Mathematique",
issn = "0021-7670",
publisher = "Hebrew University Magnes Press",
number = "1",
}