Dr. Konstantin Merz Institute of Analysis and Algebra Carl-Friedrich-Gauß-Fakultät Technische Universität Carolo-Wilhelmina Universitätsplatz 2 D-38106 Braunschweig Germany Email: k.merz(at)tu-bs.de Tel:   +49 (0)531   391 7433 Office: F 522 Since October 2022 at Department of Mathematics, Graduate School of Science, Osaka University Toyonaka, Osaka 560-0043, Japan

Research interests

• Schrödinger operators with general kinetic energies, in particular
  • eigenvalue estimates
  • heat kernel estimates
  • spectral multiplier theorems
• Functional inequalities
• Many-particle quantum systems

Publications

1. (with R. L. Frank and H. Siedentop) Equivalence of Sobolev norms involving generalized Hardy operators. Int. Math. Res. Not. 2021 (2021), no. 3, 2284-2303 - Article - Preprint
2. (with H. Siedentop) The atomic density on the Thomas-Fermi length scale for the Chandrasekhar Hamiltonian. Rep. Math. Phys. 83 (2019), no. 3, 387-391 - Article - Preprint
3. On scales of Sobolev spaces associated to generalized Hardy operators. Math. Z. 299 (2021), no. 1, 101-121 - Article - Preprint
4. (with R. L. Frank, H. Siedentop, and B. Simon) Proof of the strong Scott conjecture for Chandrasekhar atoms. Pure Appl. Funct. Anal. 5 (2020), no. 6, 1319-1356. (issue dedicated to Yakov Sinai on his 85th Birthday). - Article - Preprint
5. (with J.-C. Cuenin) Weak coupling limit for Schrödinger-type operators with degenerate kinetic energy for a large class of potentials. Lett. Math. Phys. 111 (2021), no. 2, paper number 46 - Article - Preprint
6. (with H. Siedentop) Proof of the Strong Scott Conjecture for Heavy Atoms: the Furry Picture. Ann. H. Lebesgue 5 (2022), 611-642 - Article - Preprint
7. (with R. L. Frank and H. Siedentop) Relativistic strong Scott conjecture: A short proof. In: Density Functionals for Many-Particle Systems. Mathematical Theory and Physical Applications of Effective Equations, B.-G. Englert, H. Siedentop, and M.-I. Trappe (eds.), Lect. Notes Ser. Inst. Math. Sci. Natl. Univ. Singap. 41, 69-79, World Scientific, Singapore, 2023 - Article - Preprint
8. On complex-time heat kernels of fractional Schrödinger operators via Phragmén-Lindelöf principle. J. Evol. Equ. 22 (2022), no. 3, paper number 62 - Article - Preprint
9. (with J.-C. Cuenin) Random Schrödinger operators with complex decaying potentials. Submitted - Preprint
10. (with J.-C. Cuenin) On the number and sums of eigenvalues of Schrödinger-type operators with degenerate kinetic energy. To appear in Operator Theory: Advances and Applications - Preprint
11. (with R. L. Frank and H. Siedentop) The Scott conjecture for large Coulomb systems: a review. Lett. Math. Phys. 113 (2023), paper number 11 - Article - Preprint
12. (with R. L. Frank) On Sobolev norms involving Hardy operators in a half-space. Submitted - Preprint

Seminars and conferences

GAuS online seminar (joint with Christoph Kehle and Simone Rademacher)

Minisymposium Mathematical Analysis of Complex Quantum Systems at the DMV Annual Meeting 2022 (joint with Heinz Siedentop)

Teaching / Lehre (in German)

Curriculum Vitae

Links