Rupert L. Frank

List of Publications:

1. On the scattering theory of the Laplacian with a periodic boundary condition. I. Existence of wave operators. Doc. Math. 8 (2003), 547 - 565. Article
2. (with R.G. Shterenberg) On the scattering theory of the Laplacian with a periodic boundary condition. II. Additional channels of scattering. Doc. Math. 9 (2004), 57 - 77. Article
3. On the Laplacian in the halfspace with a periodic boundary condition. Ark. Mat. 44 (2006), no. 2, 277 - 298. Article - Preprint
4. On the tunneling effect for magnetic Schrödinger operators in antidot lattices. Asymptot. Anal. 48 (2006), no. 1-2, 91 - 120. Article - Preprint
5. (with R.G. Shterenberg) On the spectrum of partially periodic operators. In: Operator Theory, Analysis and Mathematical Physics, J. Janas, et al. (eds.), 35 - 50, Oper. Theory Adv. Appl. 174, Birkhäuser, Basel, 2007. Article - Preprint
6. (with O. Safronov) Absolutely continuous spectrum of a class of random nonergodic Schrödinger operators. Int. Math. Res. Not. (2005), no. 42, 2559 - 2577. Article - Preprint
7. (with P. Exner) Absolute continuity of the spectrum for periodically modulated leaky wires in R^3. Ann. Henri Poincaré 8 (2007), no. 2, 241 - 263. Article - Preprint
8. (with T. Ekholm) On Lieb-Thirring inequalities for Schrödinger operators with virtual level. Comm. Math. Phys. 264 (2006), no. 3, 725 - 740. Article - Preprint
9. On the asymptotic number of edge states for magnetic Schrödinger operators. Proc. London Math. Soc. (3) 95 (2007), no. 1, 1 - 19. Article - Preprint
10. (with A. Laptev, E.H. Lieb and R. Seiringer) Lieb-Thirring inequalities for Schrödinger operators with complex-valued potentials. Lett. Math. Phys. 77 (2006), 309 - 316. Article - Preprint
11. (with E.H. Lieb and R. Seiringer) Hardy-Lieb-Thirring inequalities for fractional Schrödinger operators. J. Amer. Math. Soc., to appear. Preprint
12. (with E.H. Lieb and R. Seiringer) Stability of relativistic matter with magnetic fields for nuclear charges up to the critical value. Comm. Math. Phys. 275 (2007), no. 2, 479 - 489. Article - Preprint
13. (with T. Ekholm) Lieb-Thirring inequalities on the half-line with critical exponent. J. Eur. Math. Soc., to appear. Preprint
14. (with A.M. Hansson) Eigenvalue estimates for the Aharonov-Bohm operator in a domain. In: Oper. Theory Adv. Appl., to appear. Preprint
15. (with H. Siedentop and S. Warzel) The ground state energy of heavy atoms: relativistic lowering of the leading energy correction. Comm. Math. Phys., to appear. Preprint
16. (with C. Hainzl, S. Naboko and R. Seiringer) The critical temperature in the BCS model at weak coupling. J. Geom. Anal., to appear. Preprint
17. (with R.D. Benguria and M. Loss) The sharp constant in the Hardy-Sobolev-Maz'ya inequality in the three dimensional upper half-space. Math. Res. Lett., to appear. Preprint
18. (with E.H. Lieb, R. Seiringer and H. Siedentop) Müller's exchange-correlation energy in density-matrix-functional theory. Phys. Rev. A 76 (2007), 052517. Article - Preprint
19. (with A. Laptev and S. Molchanov) Eigenvalue estimates for magnetic Schrödinger operators in domains. Submitted. Preprint
20. (with B. Simon and T. Weidl) Eigenvalue bounds for perturbations of Schrödinger operators and Jacobi matrices with regular ground states. Comm. Math. Phys., to appear. Preprint
21. (with M. Loss and T. Weidl) Polya's conjecture in the presence of a constant magnetic field. Submitted. Preprint
22. (with E.H. Lieb and R. Seiringer) Number of bound states of Schrödinger operators with matrix-valued potentials. Lett. Math. Phys., to appear. Preprint
23. (with T. Ekholm and H. Kovarik) Eigenvalue estimates for Schrödinger operators on metric trees. Submitted. Preprint
24. (with T. Ekholm and H. Kovarik) Remarks about Hardy inequalities on metric trees. Submitted. Preprint
25. (with A. Laptev) Spectral inequalities for Schrödinger operators with surface potentials. Submitted. Preprint