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A New Life of the Classical Szegő Formula

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Extended Abstracts Fall 2019

Part of the book series: Trends in Mathematics ((RPCRMB,volume 12))

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Abstract

We collect several applications of a new version of the classical Szegő formula for orthogonal polynomials. The applications are concerned with the spectral theory of Krein strings, scattering theory for Dirac systems, and triangular factorizations of positive Wiener–Hopf operators.

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References

  1. R.V. Bessonov, S.A. Denisov, A spectral Szegő theorem on the real line. Adv. Math. 359, 1–41 (2020)

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  2. R.V. Bessonov, Wiener-Hopf operators admit triangular factorization. J. Oper. Theory 82(1), 237–249 (2019)

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  3. R.V. Bessonov, Szegő condition and scattering for one-dimensional Dirac operators. Constr. Approx. 51, 273–302 (2020)

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  4. R.V. Bessonov, S.A. Denisov, Zero sets, entropy, and pointwise asymptotics of orthogonal polynomials. Arxiv preprint arXiv:1911.11280

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Acknowledgements

The work is supported by grant RScF 19-11-00058.

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Authors and Affiliations

  1. St. Petersburg State University, Universitetskaya nab. 7-9, 199034, St. Petersburg, Russia

    Roman Bessonov

  2. St. Petersburg Department of Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, 191023, St. Petersburg, Russia

    Roman Bessonov

  3. Department of Mathematics, University of Wisconsin–Madison, 480 Lincoln Dr., Madison, WI, 53706, USA

    Sergey Denisov

  4. Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Miusskaya pl. 4, 125047, Moscow, Russia

    Sergey Denisov

Authors
  1. Roman Bessonov
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  2. Sergey Denisov
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Corresponding author

Correspondence to Sergey Denisov .

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Editors and Affiliations

  1. Laboratoire d'Analyse et de Mathématiques Appliquées, Université Gustave Eiffel, Marne-la-Vallée, France

    Evgeny Abakumov

  2. Department of Mathematics and Mechanics, St. Petersburg State University, St. Petersburg, Russia

    Anton Baranov

  3. Institut de Mathématiques de Marseille, Aix Marseille Université, Marseille, France

    Alexander Borichev

  4. Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia

    Konstantin Fedorovskiy

  5. Departament de Matemàtiques i Informàtica, Universitat de Barcelona, Barcelona, Spain

    Joaquim Ortega-Cerdà

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Bessonov, R., Denisov, S. (2021). A New Life of the Classical Szegő Formula. In: Abakumov, E., Baranov, A., Borichev, A., Fedorovskiy, K., Ortega-Cerdà, J. (eds) Extended Abstracts Fall 2019. Trends in Mathematics(), vol 12. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-74417-5_5

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