Wissenschaftliche Interessen

• Operatortheorie
• Spektraltheorie
• Differentialoperatoren
• Mathematische Physik

Publikationen

Artikel in referierten Zeitschriften:

1. The abstract Birman–Schwinger principle and spectral stability,
   gemeinsam mit 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,
   gemeinsam mit C. Rose und 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,
   gemeinsam mit M. Demuth, F. Hanauska und 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,
    gemeinsam mit M. Demuth und G.Katriel,
    Int. Eq. Op. Theory, 75(1) (2013) 1-5, Open Problems.
11. Eigenvalues of non-selfadjoint operators: a comparison of two approaches,
    gemeinsam mit M. Demuth und 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,
    gemeinsam mit 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,
    gemeinsam mit G. Katriel,
    Complex Anal. Oper. Theory, 5(1) (2011) 197-218. arXiv-Preprint: 0901.1725.
17. On the discrete spectrum of non-selfadjoint operators,
    gemeinsam mit M. Demuth und 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,
    gemeinsam mit 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.

Konferenzbände:

1. On the role of the comparison function in the spectral theory of selfadjoint operators,
   gemeinsam mit 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.

Mathematische Berichte:

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

Abschlussarbeiten:

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