A relation between the positive and negative spectra of elliptic operators

DOI10.1007/S11005-017-0970-YOpenAlexW2615240285MaRDI QIDQ2410935

Oleg Safronov, Rowan Killip, Stanislav Alekseevich Molchanov

Publication date: 20 October 2017

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11005-017-0970-y

zbMATH Keywords

continuous spectrumSchrödinger operatorsdiscrete spectrumsingular sequences

Mathematics Subject Classification ID

General theory of partial differential operators (47F05) Schrödinger operator, Schrödinger equation (35J10) Higher-order elliptic equations (35J30)

Related Items (2)

The rate of accumulation of negative eigenvalues to zero and the absolutely continuous spectrum ⋮ Relations between two parts of the spectrum of a Schrödinger operator and other remarks on the absolute continuity of the spectrum in a typical case

Cites Work

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• Lower bounds on the eigenvalue sums of the Schrödinger operator and the spectral conservation law
• Absolutely continuous spectrum of a Dirac operator in the case of a positive mass
• Half-line Schrödinger operators with no bound states
• Schrödinger operators with many bound states
• Variational estimates for discrete Schrödinger operators with potentials of indefinite sign
• Sum rules for Jacobi matrices and their applications to spectral theory
• Multi-dimensional Schrödinger operators with no negative spectrum
• Multi-dimensional Schrödinger operators with some negative spectrum

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