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. 21 (2008), no. 4, 925 - 950. Article - 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. 10 (2008), no. 3, 739 - 755. Article - Preprint
  14. (with A.M. Hansson) Eigenvalue estimates for the Aharonov-Bohm operator in a domain. In: Methods of Spectral Analysis in Mathematical Physics, J. Janas, et al. (eds.), 35 - 50, Oper. Theory Adv. Appl. 186, Birkhäuser, Basel, 2008. Article - 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. 278 (2008), no. 2, 549 - 566. Article - Preprint
  16. (with C. Hainzl, S. Naboko and R. Seiringer) The critical temperature in the BCS model at weak coupling. J. Geom. Anal. 17 (2007), no. 4, 559 - 568. Article - 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. 15 (2008), no. 4, 613 - 622. Article - 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. Proc. Amer. Math. Soc. 136 (2008), no. 12, 4245 - 4255. Article - 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. 282 (2008), no. 1, 199 - 208. Article - Preprint
  21. (with M. Loss and T. Weidl) Polya's conjecture in the presence of a constant magnetic field. J. Eur. Math. Soc. 11 (2009), 1365 - 1383. Article - Preprint
  22. (with E.H. Lieb and R. Seiringer) Number of bound states of Schrödinger operators with matrix-valued potentials. Lett. Math. Phys. 82 (2007), 107 - 116. Article - 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. In: Analysis on graphs and its applications, P. Exner, et al. (eds.), 369 - 379, Proc. Sympos. Pure Math. 77, Amer. Math. Soc., Providence, RI, 2008. Preprint
  25. (with A. Laptev) Spectral inequalities for Schrödinger operators with surface potentials. In: Spectral theory of differential operators, T. Suslina and D. Yafaev (eds.), 91 - 102, Amer. Math. Soc. Transl. Ser. 2, 225 (2008). Preprint
  26. (with R. Seiringer) Non-linear ground state representations and sharp Hardy inequalities. J. Funct. Anal. 255 (2008), 3407 - 3430. Article - Preprint
  27. (with H. Siedentop and S. Warzel) The energy of heavy atoms according to Brown and Ravenhall: the Scott correction. Doc. Math., to appear. Preprint
  28. (with J. Breuer) Singular spectrum for radial trees. Rev. Math. Phys. 21 (2009), no. 7, 1 - 17. Preprint
  29. A simple proof of Hardy-Lieb-Thirring inequalities. Comm. Math. Phys. 290 (2009), no. 2, 789 - 800. Article - Preprint
  30. A note on low energy scattering for homogeneous long-range potentials. Ann. Henri Poincaré 10 (2009), no. 3, 573 - 575. Article - Preprint
  31. Remarks on eigenvalue estimates and semigroup domination. In: Spectral and Scattering Theory for Quantum Magnetic Systems, P. Briet, et al. (eds.), 63 - 86, Contemp. Math. 500, Amer. Math. Soc., Providence, RI, 2009. Preprint
  32. (with A. Laptev and R. Seiringer) A sharp bound on eigenvalues of Schrödinger operators on the halfline with complex-valued potentials. In: Oper. Theory Adv. Appl., to appear. Preprint
  33. (with S. Morozov and S. Vugalter) Weakly coupled bound states of Pauli operators. Submitted. Preprint
  34. (with E.H. Lieb) Inversion positivity and the sharp Hardy-Littlewood-Sobolev inequality. Submitted. Preprint
  35. (with E. Lenzmann) Uniqueness of ground states for the L^2-critical boson star equation. Submitted. Preprint
  36. (with R. Seiringer) Sharp fractional Hardy inequalities in half-spaces. In: Around the research of Vladimir Maz'ya, A. Laptev (ed.), 161 - 167, International Mathematical Series 11 (2010). Article - Preprint
  37. (with A. Laptev) Inequalities between Dirichlet and Neumann eigenvalues on the Heisenberg group. Submitted. Preprint
  38. (with E.H. Lieb and R. Seiringer) Equivalence of Sobolev inequalities and Lieb-Thirring inequalities. Submitted. Preprint
  39. (with E. Lenzmann) Uniqueness and symmetry of ground states for the L^2-critical boson star equation. Submitted. Preprint


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Last modified: November 17, 2009