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Estimates of 1D resonances in terms of potentials

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Abstract

We discuss resonances for Schrödinger operators with compactly supported potentials on the line and the half-line. We estimate the sum of the negative power of all resonances and eigenvalues in terms of the norm of the potential and the diameter of its support. The proof is based on harmonic analysis and Carleson measures arguments.

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Authors and Affiliations

  1. Saint-Petersburg State University, Universitetskaya Nab. 7/9, St. Petersburg, 199034, Russia

    Evgeny Korotyaev

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  1. Evgeny Korotyaev
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Correspondence to Evgeny Korotyaev.

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Dedicated to Lennart Carleson, on the occasion of his 85th birthday

This work was supported by the RFFI grant No. 16-01-00087, the Russian foundation of basic research under grant No. 14-01-00760-a, and the SPbGU grant No. 11.42.1063.2016.

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Korotyaev, E. Estimates of 1D resonances in terms of potentials. JAMA 130, 151–166 (2016). https://doi.org/10.1007/s11854-016-0032-x

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  • DOI: https://doi.org/10.1007/s11854-016-0032-x

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