Lukas Schimmer

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. (with A. Laptev) A sharp Lieb–Thirring inequality for functional difference operators,
   SIGMA 17, 105, 10 pages (2021). Preprint, Article
   
   
8. (with A. Laptev and M. Loss) On a Conjecture by Hundertmark and Simon,
   Ann. Henri Poincaré 23: 4057–4067 (2022). Preprint, Article
   
   
9. (with A. Laptev and L. Read) Calogero type bounds in two dimensions,
   Arch. Ration. Mech. Anal. 245: 1491–1505 (2022). Preprint, Article
   
   
10. The state of the Lieb–Thirring conjecture,
    In: The Physics and Mathematics of Elliott Lieb. 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
    
    
11. Improved sharp spectral inequalities for Schrödinger operators on the semi-axis,
    J. Spectr. Theory 13(1): 47–62 (2023). Preprint, Article
    
    
12. (with A. Ilyin, A. Laptev and A. Zernova) Eigenvalues of non-selfadjoint functional difference operators,
    submitted (2025). Preprint
    
    

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