Lukas Schimmer

Lecturer in Mathematics at Loughborough University

You may also find my research outputs on my ORCID record.

Articles:

  1. The Berezin inequality on domains of infinite measure,
    Bull. Math. Sci. 3(1): 173-182 (2013). Article

  2. Spectral inequalities for Jacobi operators and related sharp Lieb–Thirring inequalities on the continuum,
    Commun. Math. Phys. 334(1): 473-505 (2015). Preprint, Article

  3. (with A. Laptev and L. A. Takhtajan) Weyl type asymptotics and bounds for the eigenvalues of functional-difference operators for mirror curves,
    Geom. Funct. Anal. 26(1): 288-305 (2016). Preprint, Article

  4. (with R. L. Frank) Endpoint resolvent estimates for compact Riemannian manifolds,
    J. Funct. Anal. 272(9): 3904-3918 (2017). Preprint, Article

  5. (with A. Laptev and L. A. Takhtajan) Weyl asymptotics for perturbed functional difference operators,
    J. Math. Phys 60(10): 103505 (2019). Article

  6. (with J. P. Solovej and S. Tokus) Friedrichs Extension and Min-Max Principle for Operators with a Gap,
    Ann. Henri Poincaré 21: 327-357 (2020). Preprint, Article

  7. Improved sharp spectral inequalities for Schrödinger operators on the semi-axis,
    to appear in J. Spectr. Theory (2022). Preprint

  8. (with A. Laptev) A sharp Lieb–Thirring inequality for functional difference operators,
    SIGMA 17, 105, 10 pages (2021). Preprint, Article

  9. (with A. Laptev and M. Loss) On a Conjecture by Hundertmark and Simon,
    to appear in Ann. Henri Poincaré 23: 4057-4067 (2022). Preprint, Article

  10. (with A. Laptev and L. Read) Calogero type bounds in two dimensions,
    Arch. Ration. Mech. Anal. 245: 1491-1505 (2022). Preprint, Article

  11. The state of the Lieb–Thirring conjecture,
    to appear in a book in honour of Elliott H. Lieb's 90th birthday, edited by R. L. Frank, A. Laptev, M. Lewin and R. Seiringer, EMS Publishing House (2022). Preprint, Article

PhD Thesis:

Spectral Inequalities for Discrete and Continuous Differential Operators, Thesis, 2014.

Lecture Notes:

The Stability of Matter in non-relativistic Quantum Mechanics, Lecture notes for Advanced Mathematical Physics at the University of Copehagen, 2018.

Other:

I am the author of two Wikipedia articles on topics related to my research.

Lieb–Thirring inequality

Lieb–Oxford inequality