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Weyl’s Law under Minimal Assumptions

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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))

Abstract

We show that Weyl’s law for the number and the Riesz means of negative eigenvalues of Schrödinger operators remains valid under minimal assumptions on the potential, the vector potential and the underlying domain.

Dedicated to the memory of Sergey Naboko

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Acknowledgements

Partial support through U.S. National Science Foundation grant DMS-1954995 and through the German Research Foundation grant EXC-2111-390814868 is acknowledged.

Author information

Authors and Affiliations

  1. Mathematisches Institut, Ludwig-Maximilans Universität München, München, Germany

    Rupert L. Frank

  2. Munich Center for Quantum Science and Technology, München, Germany

    Rupert L. Frank

  3. Mathematics 253-37, Caltech, Pasadena, CA, USA

    Rupert L. Frank

Authors
  1. Rupert L. Frank
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Correspondence to Rupert L. Frank .

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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Frank, R.L. (2023). Weyl’s Law under Minimal Assumptions. 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_20

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