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Sergey Naboko’s Legacy on the Spectral Theory of Jacobi Operators

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From Complex Analysis to Operator Theory: A Panorama

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 291))

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Abstract

Sergey Naboko authored a large amount of papers on the spectral theory of Jacobi operators. The main themes of his work are the existence of eigenvalues embedded into the absolutely continuous spectrum; spectral phase transitions for specifically-chosen Jacobi matrices, where new asymptotic methods for spectral analysis were established; construction of Jacobi matrices with gaps in the essential spectrum; estimates of Green matrix for Jacobi operators, and inverse resonance problems. In his later years, Sergey Naboko worked on block Jacobi matrices where he found realizations having both similar and dissimilar properties to their scalar counterparts.

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References

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Author information

Authors and Affiliations

  1. Departamento de Física Matemática, Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, Mexico City, México

    Luis O. Silva

  2. St. Petersburg Department of V.A. Steklov Institute of Mathematics of the Russian Academy of Sciences, St Petersburg, Russia

    Sergey Simonov

  3. St. Petersburg State University, Universitetskaya nab. 7–9, St. Petersburg, Russia

    Sergey Simonov

  4. Alferov University, St. Petersburg, Russia

    Sergey Simonov

Authors
  1. Luis O. Silva
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  2. Sergey Simonov
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Correspondence to Luis O. Silva .

Editor information

Editors and Affiliations

  1. School of Computer Science & Informatics, Cardiff University, Cardiff, UK

    Malcolm Brown

  2. Department of Mathematics, Baylor University, Waco, TX, USA

    Fritz Gesztesy

  3. Department of Mathematics, Stockholm University, Stockholm, Sweden

    Pavel Kurasov

  4. Department of Mathematics Imperial College London London, United Kingdom, Sirius Mathematical Center, Sochi, Russia

    Ari Laptev

  5. Division of Physics, Mathematics and Astronomy, California Institute of Technology, Pasadena, CA, USA

    Barry Simon

  6. Department of Mathematics, University of Alabama at Birmingham, Birmingham, AL, USA

    Gunter Stolz

  7. School of Mathematics, Statistics and Actuarial Sciences, University of Kent, Canterbury, UK

    Ian Wood

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Silva, L.O., Simonov, S. (2023). Sergey Naboko’s Legacy on the Spectral Theory of Jacobi Operators. In: Brown, M., et al. From Complex Analysis to Operator Theory: A Panorama. Operator Theory: Advances and Applications, vol 291. Birkhäuser, Cham. https://doi.org/10.1007/978-3-031-31139-0_5

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