Scientific interests

• Operator Theory
• Spectral Theory
• Differential Operators
• Mathematical Physics

Publications

Articles in refereed journals:

1. The abstract Birman–Schwinger principle and spectral stability,
   joint with D. Krejcirik,
   Journal d'Analyse Mathématique, 148 (2022) 361-398. arXiv-Preprint: 2010.15102.
2. Bounds on the first Betti number - an approach via Schatten norm estimates on semigroup differences,
   joint with C. Rose and P. Stollmann,
   The Journal of Geometric Analysis, 32(115) (2022). arXiv-Preprint: 1810.12205.
3. Lp-spectrum and Lieb-Thirring inequalities for Schrödinger operators on the hyperbolic plane,
   Annales Henri Poincaré, 20(7) (2019) 2447-2479. arXiv-Preprint: 1810.00733.
4. Eigenvalues of compactly perturbed operators via entropy numbers,
   J. Spectr. Theory, 10(1) (2020) 251-269. arXiv-Preprint: 1710.01633.
5. Some remarks on upper bounds for Weierstrass primary factors and their application in spectral theory,
   Complex Anal. Oper. Theory, 11(6) (2017) 1467–1476. arXiv-Preprint: 1704.01810.
6. Perturbation determinants in Banach spaces - with an application to eigenvalue estimates for perturbed operators,
   Math. Nachr., 289(13) (2016) 1606-1625. arXiv-Preprint: 1507.06816.
7. Estimating the number of eigenvalues of linear operators on Banach spaces,
   joint with M. Demuth, F. Hanauska and G.Katriel,
   J. Funct. Anal., 268 (2015) 1032-1052. arXiv-Preprint: 1409.8569.
8. An observation concerning boundary points of the numerical range,
   Oper. Matrices, 9(3) (2015) 545-548. arXiv-Preprint: 1409.4558.
9. On non-round points of the boundary of the numerical range and an application to non-selfadjoint Schrödinger operators,
   J. Spectr. Theory, 5(4) (2015) 731–750. arXiv-Preprint: 1404.3960.
10. Lieb–Thirring Type Inequalities for Schrödinger Operators with a Complex-Valued Potential,
    joint with M. Demuth and G.Katriel,
    Int. Eq. Op. Theory, 75(1) (2013) 1-5, Open Problems.
11. Eigenvalues of non-selfadjoint operators: a comparison of two approaches,
    joint with M. Demuth and G. Katriel,
    Operator Theory: Advances and Applications, Vol. 232, 107-163. arXiv-Preprint: 1209.0266.
12. Variation of discrete spectra for non-selfadjoint perturbations of selfadjoint operators,
    Int. Eq. Op. Theory, 76(1) (2013) 163-178. arXiv-Preprint: 1202.1118.
13. Absence of eigenvalues of non-selfadjoint Schrödinger operators on the boundary of their numerical range,
    Proc. Amer. Math. Soc., 142 (2014), 1321-1335. arXiv-Preprint: 1108.1279.
14. From spectral theory to bounds on zeros of holomorphic functions,
    joint with G. Katriel,
    Bull. Lond. Math. Soc., 45(1) (2013) 103-110. arXiv-Preprint: 1103.1487.
15. An eigenvalue estimate and its application to non-selfadjoint Jacobi and Schrödinger operators,
    Lett. Math. Phys., 98(1) (2011) 79-95. arXiv-Preprint: 1006.5308.
16. Inequalities for the eigenvalues of non-selfadjoint Jacobi operators,
    joint with G. Katriel,
    Complex Anal. Oper. Theory, 5(1) (2011) 197-218. arXiv-Preprint: 0901.1725.
17. On the discrete spectrum of non-selfadjoint operators,
    joint with M. Demuth and G.Katriel,
    J. Funct. Anal., 257 (2009) 2742-2759. arXiv-Preprint: 0908.2188.
18. On spectral stability for the fractional Laplacian perturbed by unbounded obstacles,
    joint with M. Demuth,
    Math. Nachr., 282(9) (2009) 1265-1277.
19. Estimating eigenvalue moments via Schatten norm bounds on semigroup differences,
    Math. Phys. Anal. Geom., 10(3) (2007) 261-270.

Proceedings:

1. On the role of the comparison function in the spectral theory of selfadjoint operators,
   joint with M. Demuth,
   Commun. Math. Anal., Conf. 03 (2011) 77-87, Proceedings of the conference "Analysis, Mathematical Physics and Applications" in Ixtapa, Mexico, March 1-5, 2010.

Mathematical reports:

1. On the distribution of eigenvalues of non-selfadjoint operators,
   joint with M. Demuth and G. Katriel,
   TU Clausthal Mathematik Bericht 01/08. arXiv-Preprint: 0802.2468.

Theses:

1. Schrödinger-Operatoren mit großen Kopplungen – exakte Konvergenzraten,
   Diplomarbeit, TU Clausthal 2005.
2. On the discrete spectrum of linear operators in Hilbert spaces,
   Dissertation, TU Clausthal 2010. Elektronische Version
3. Eigenvalues of compactly perturbed linear operators,
   Habilitation, TU Chemnitz 2018. Elektronische Version