Rupert L. Frank
List of Publications:
 On the scattering theory of the Laplacian with a periodic
boundary condition. I. Existence of wave operators. Doc. Math.
8 (2003), 547  565. Article
 (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
 On the Laplacian in the halfspace with a periodic boundary
condition. Ark. Mat. 44 (2006), no.
2, 277
 298. Article
 Preprint
 On the tunneling effect for magnetic Schrödinger operators
in antidot lattices. Asymptot. Anal. 48
(2006), no. 12, 91  120. Article
 Preprint
 (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

(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
 (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
 (with T. Ekholm) On LiebThirring inequalities for
Schrödinger operators with virtual level. Comm. Math. Phys.
264 (2006), no. 3, 725  740.
Article
 Preprint
 On the asymptotic number of edge states for magnetic
Schrödinger operators.
Proc. London Math. Soc. (3) 95 (2007),
no. 1, 1  19.
Article
 Preprint
 (with A. Laptev, E.H. Lieb and R. Seiringer)
LiebThirring inequalities for Schrödinger operators with
complexvalued potentials.
Lett. Math. Phys. 77 (2006), 309  316.
Article 
Preprint
 (with E.H. Lieb and R. Seiringer) HardyLiebThirring
inequalities for fractional Schrödinger operators. J. Amer. Math. Soc. 21 (2008), no. 4, 925  950.
Article 
Preprint
 (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
 (with T. Ekholm) LiebThirring inequalities on the
halfline with critical exponent. J. Eur. Math. Soc. 10 (2008), no. 3, 739  755.
Article 
Preprint
 (with A.M. Hansson)
Eigenvalue estimates for the AharonovBohm 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
 (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
 (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
 (with R.D. Benguria and M. Loss)
The sharp constant in the HardySobolevMaz'ya inequality in the three
dimensional upper halfspace.
Math. Res. Lett. 15 (2008), no. 4, 613  622.
Article
 Preprint
 (with E.H. Lieb, R. Seiringer and H. Siedentop)
Müller's exchangecorrelation energy in densitymatrixfunctional theory.
Phys. Rev. A 76 (2007), 052517.
Article 
Preprint
 (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
 (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

(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
 (with E.H. Lieb and R. Seiringer)
Number of bound states of Schrödinger operators with matrixvalued potentials.
Lett. Math. Phys. 82 (2007), 107  116.
Article 
Preprint
 (with T. Ekholm and H. Kovarik)
Eigenvalue estimates for Schrödinger operators on metric trees.
Adv. Math. 226 (2011), 5165  5197.
Article 
Preprint
 (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
 (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
 (with R. Seiringer)
Nonlinear ground state representations and sharp Hardy inequalities.
J. Funct. Anal. 255 (2008), 3407  3430.
Article 
Preprint

(with H. Siedentop and S. Warzel)
The energy of heavy atoms according to Brown and Ravenhall: the Scott correction.
Doc. Math. 14 (2009), 463  516.
Article 
Preprint

(with J. Breuer)
Singular spectrum for radial trees.
Rev. Math. Phys. 21 (2009), no. 7, 1  17.
Article 
Preprint

A simple proof of HardyLiebThirring inequalities.
Comm. Math. Phys. 290 (2009), no. 2, 789  800.
Article 
Preprint

A note on low energy scattering for homogeneous longrange potentials.
Ann. Henri Poincaré 10 (2009), no. 3, 573  575.
Article 
Preprint

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

(with A. Laptev and R. Seiringer)
A sharp bound on eigenvalues of Schrödinger operators on the halfline with complexvalued potentials.
In: Spectral Theory and Analysis, J. Janas et al. (eds.), 39  44,
Oper. Theory Adv. Appl. 214, Birkhäuser, Basel, 2011.
Article 
Preprint

(with S. Morozov and S. Vugalter)
Weakly coupled bound states of Pauli operators.
Calc. Var. Partial Differential Equations 40 (2010), no. 1  2, 253  271.
Article 
Preprint

(with E.H. Lieb)
Inversion positivity and the sharp HardyLittlewoodSobolev inequality.
Calc. Var. Partial Differential Equations 39 (2010), no. 1  2, 85  99.
Article 
Preprint

(with R. Seiringer)
Sharp fractional Hardy inequalities in halfspaces.
In: Around the research of Vladimir Maz'ya, A. Laptev (ed.),
161  167, International Mathematical Series 11 (2010).
Article 
Preprint

(with A. Laptev)
Inequalities between Dirichlet and Neumann eigenvalues on the Heisenberg group.
Int. Math. Res. Not. 15 (2010), 2889  2902.
Article 
Preprint

(with E.H. Lieb and R. Seiringer)
Equivalence of Sobolev inequalities and LiebThirring inequalities.
In: XVIth International Congress on Mathematical Physics, Proceedings of the ICMP held in Prague, August 38, 2009, P. Exner (ed.), 523535, World Scientific, Singapore, 2010.
Article 
Preprint

(with B. Simon)
Critical LiebThirring bounds in gaps and the generalized Nevai conjecture for finite gap Jacobi matrices.
Duke Math. J. 157 (2011), no. 3, 461  493.
Article 
Preprint

(with E.H. Lieb)
Spherical reflection positivity and the HardyLittlewoodSobolev inequality.
In: Concentration, Functional Inequalities and Isoperimetry, C. Houdré et al. (eds.), Contemp. Math. 545, Amer. Math. Soc., Providence, RI, 2011.
Article 
Preprint

(with E.H. Lieb, R. Seiringer and L.E. Thomas)
Bipolaron and Npolaron binding energies.
Phys. Rev. Lett. 104 (2010), 210402.
Article 
Preprint

(with E.H. Lieb, R. Seiringer and L.E. Thomas)
Stability and absence of binding for multipolaron systems.
Publ. Math. IHES 113 (2011), no. 1, 39  67.
Article 
Preprint

Eigenvalue bounds for Schrödinger operators with complex potentials.
Bull. Lond. Math. Soc. 43 (2011), no. 4, 745  750.
Article 
Preprint

(with E.H. Lieb)
Sharp constants in several inequalities on the Heisenberg group.
Ann. of Math. 176 (2012), no. 1, 349  381.
Article

Preprint

(with E. Lenzmann)
Uniqueness and nondegeneracy of ground states for (\Delta)^s Q + Q  Q^{\alpha+1} = 0 in R.
Acta Math. 210 (2013), no. 2, 261  318.
Article 
Preprint

(with E.H. Lieb, R. Seiringer and L.E. Thomas)
Binding, stability and nonbinding of multipolaron systems.
In: Mathematical results in quantum physics, Proceedings of the QMath11
Conference, P. Exner (ed.), 21  32, World Scientific, Singapore, 2011.
Article 
Preprint

(with L. Geisinger)
Twoterm spectral asymptotics for the Dirichlet Laplacian on a bounded domain.
In: Mathematical results in quantum physics, Proceedings of the QMath11
Conference, P. Exner (ed.), 138  147, World Scientific, Singapore, 2011.
Article 
Preprint

(with E.H. Lieb)
A new, rearrangementfree proof of the sharp HardyLittlewoodSobolev inequality.
In: Spectral Theory, Function Spaces and Inequalities, B. M. Brown et al.
(eds.), 55  67, Oper. Theory Adv. Appl. 219, Birkhäuser, Basel,
2012.
Article 
Preprint

(with D. Lenz and D. Wingert)
Intrinsic metrics for nonlocal symmetric Dirichlet forms and applications to spectral theory.
J. Funct. Anal. 266 (2014), no. 8, 4765  4808.
Article 
Preprint

(with R. Olofsson)
Eigenvalue bounds for Schrödinger operators with a homogeneous magnetic field.
Lett. Math. Phys. 97 (2011), no. 3, 227  241,
Article 
Preprint

(with M. Lewin, E.H. Lieb and R. Seiringer)
Energy cost to make a hole in the Fermi sea.
Phys. Rev. Lett. 106 (2011), 150402.
Article 
Preprint

(with C. Hainzl, R. Seiringer and J.P. Solovej)
Microscopic derivation of GinzburgLandau theory.
J. Amer. Math. Soc. 25 (2012), no. 3, 667  713.
Article 
Preprint

(with M. Loss)
HardySobolevMaz'ya inequalities for arbitrary domains.
J. Math. Pures Appl. 97 (2012), 39  54.
Article 
Preprint

(with C. Hainzl, R. Seiringer and J.P. Solovej)
Derivation of GinzburgLandau theory for a onedimensional system with contact interaction.
In: Operator Methods in Mathematical Physics, J. Janas et al. (eds.), 57  88,
Oper. Theory Adv. Appl. 227, Birkhäuser, Basel, 2013.
Article 
Preprint

(with E.H. Lieb)
Possible lattice distortions in the Hubbard model for graphene.
Phys. Rev. Lett. 107 (2011), 066801.
Article 
Preprint

(with L. Geisinger)
Refined semiclassical asymptotics for fractional powers of the Laplace operator.
J. Reine Angew. Math. 712 (2016), 1  37.
Article 
Preprint

(with E.H. Lieb and R. Seiringer)
Binding of polarons and atoms at threshold.
Comm. Math. Phys. 313 (2012), no. 2, 405  424.
Article 
Preprint

(with H.D. Cornean, S. Fournais and B. Helffer)
Sharp trace asymptotics for a class of 2Dmagnetic operators.
Ann. Inst. Fourier (Grenoble) 63 (2013), no. 6, 2457  2513.
Article 
Preprint

(with M. Lewin, E.H. Lieb and R. Seiringer)
A positive density analogue of the LiebThirring inequality.
Duke Math. J. 162 (2013), no. 3, 435  495.
Article 
Preprint

(with H. Kovarik)
Heat kernels of metric trees and applications.
SIAM J. Math. Anal. 45 (2013), no. 3, 1027  1046.
Article 
Preprint

(with E.H. Lieb)
Entropy and the uncertainty principle.
Ann. Henri Poincaré 13 (2012), no. 8, 1711  1717.
Article 
Preprint

On the uniqueness of ground states of nonlocal equations.
Journées Équations aux Dérivées Partielles 2011, Exp. No. V, 10 pp.
Article 
Preprint

(with B. Dyda)
Fractional HardySobolevMaz'ya inequality for domains.
Studia Math. 208 (2012), no. 2, 151  166.
Article 
Preprint

(with R. Seiringer)
LiebThirring inequality for a model of particles with point interactions.
J. Math. Phys. 53 (2012), no. 9, 095201.
Article 
Preprint

(with E.H. Lieb and R. Seiringer)
Symmetry of bipolaron bound states for small Coulomb repulsion.
Comm. Math. Phys. 319 (2013), no. 2, 557  573.
Article 
Preprint

(with E.H. Lieb)
Extended quantum conditional entropy and quantum uncertainty inequalities.
Comm. Math. Phys. 323 (2013), no. 2, 487  495.
Article 
Preprint

(with S. Chen and T. Weth)
Remainder terms in the fractional Sobolev inequality.
Indiana Univ. Math. J. 62 (2013), 1381  1397.
Article 
Preprint

Cwikel's theorem and the CLR inequality.
J. Spectr. Theory 4 (2014), no. 1, 1  21.
Article 
Preprint

(with L. Geisinger)
Semiclassical analysis of the Laplace operator with Robin boundary conditions.
Bull. Math. Sci. 2 (2012), no. 2, 281  319.
Article 
Preprint

(with C. Hainzl, R. Seiringer and J.P. Solovej)
Microscopic derivation of the GinzburgLandau model.
In: XVIIth International Congress on Mathematical Physics, Proceedings of the ICMP held in Aalborg, August 611, 2012, A. Jensen (ed.), 575583, World Scientific, Singapore, 2013.
Article 
Preprint

(with E.H. Lieb, R. Seiringer and L.E. Thomas)
Ground state properties of multipolaron systems.
In: XVIIth International Congress on Mathematical Physics, Proceedings of the ICMP held in Aalborg, August 611, 2012, A. Jensen (ed.), 477485, World Scientific, Singapore, 2013.
Article 
Preprint

(with E.A. Carlen and E.H. Lieb)
Stability estimates for the lowest eigenvalue of a Schrödinger operator.
Geom. Funct. Anal. 24 (2014), no. 1, 63  84.
Article 
Preprint

(with J. Bellazzini, E.H. Lieb and R. Seiringer)
Existence of ground states for negative ions at the binding threshold.
Rev. Math. Phys. 26 (2014), no. 1, 1350021.
Article 
Preprint

(with E. Lenzmann and L. Silvestre)
Uniqueness of radial solutions for the fractional Laplacian.
Comm. Pure Appl. Math. 69 (2016), no. 9, 1671  1726.
Article 
Preprint

(with L. Geisinger)
The ground state energy of a polaron in a strong magnetic field.
Comm. Math. Phys. 338 (2015), no. 1, 1  29.
Article 
Preprint

(with M. Lewin, E.H. Lieb and R. Seiringer)
Strichartz inequality for orthonormal functions.
J. Eur. Math. Soc. 16 (2014), no. 7, 1507  1526.
Article 
Preprint

(with E.H. Lieb)
Monotonicity of a relative Rényi entropy.
J. Math. Phys. 54 (2013), 122201.
Article 
Preprint

(with J. Bellazzini and N. Visciglia)
Maximizers for GagliardoNirenberg inequalities and related nonlocal problems.
Math. Ann. 360 (2014), no. 34, 653  673.
Article 
Preprint

(with B. Schlein)
Dynamics of a strongly coupled polaron.
Lett. Math. Phys. 104 (2014), no. 8, 911  929.
Article 
Preprint

(with M. d. M. Gonzalez, D. D. Monticelli and J. Tan)
An extension problem for the CR fractional Laplacian.
Adv. Math. 270 (2015), 97  137.
Article 
Preprint

(with T. Ekholm and H. Kovarik)
Weak perturbations of the pLaplacian.
Calc. Var. Partial Differential Equations 53 (2015), 781  801.
Article 
Preprint

(with A. Pushnitski)
Trace class conditions for functions of Schrödinger operators.
Comm. Math. Phys. 335 (2015), 477  496.
Article 
Preprint

(with J. Sabin)
Restriction theorems for orthonormal functions, Strichartz inequalities, and uniform Sobolev estimates.
Amer. J. of Math. 139 (2017), no. 6, 1649  1691.
Article 
Preprint

(with E. A. Carlen and E. H. Lieb)
Some operator and trace function convexity theorems.
Linear Algebra Appl. 490 (2016), 174  185.
Article 
Preprint

(with A. Pushnitski)
The spectral density of a product of spectral projections.
J. Funct. Anal. 268 (2015), 3867  3894.
Article 
Preprint

(with R. D. Benguria and E. H. Lieb)
Ground state energy of large polaron systems.
J. Math. Phys. 56 (2015), 021901.
Article 
Preprint

(with C. Hainzl, R. Seiringer and J. P. Solovej)
The external field dependence of the BCS critical temperature.
Comm. Math. Phys. 342 (2016), no. 1, 189  216.
Article 
Preprint

(with E. H. Lieb)
A compactness lemma and its application to the existence of minimizers for the liquid drop model.
SIAM J. Math. Anal. 47 (2015), no. 6, 4436  4450.
Article 
Preprint

(with B. Simon)
Eigenvalue bounds for Schrödinger operators with complex potentials. II.
J. Spectr. Theory 7 (2017), no. 3, 633  658.
Article 
Preprint

(with C. Hainzl, B. Schlein and R. Seiringer)
Timedependent BogolubovdeGennes equations and nonvalidity of GinzburgLandau theory.
Lett. Math. Phys. 106 (2016), no. 7, 913  923.
Article 
Preprint

(with M. Lemm)
GinzburgLandau theory with multiple order parameters: microscopic derivation and examples.
Ann. H. Poincaré 17 (2016), no. 9, 2285  2340.
Article 
Preprint

(with Z. Gang)
Derivation of an effective evolution equation for a strongly coupled polaron.
Anal. PDE 10 (2017), no. 2, 379  422.
Article 
Preprint

Eigenvalue bounds for Schrödinger operators with complex potentials. III.
Trans. Amer. Math. Soc. 370 (2018), no. 1, 219  240.
Article 
Preprint

Eigenvalues of Schrödinger operators with complex surface potentials.
In: Functional Analysis and Operator Theory for Quantum Physics, J. Dittrich, et al. (eds.), 245  260. EMS, 2017.
Article 
Preprint

(with A. Laptev, O. Safronov)
On the number of eigenvalues of Schrödinger operators with complex potentials.
J. Lond. Math. Soc. (2) 94 (2016), no. 2, 377  390.
Article 
Preprint

(with J. Behrndt, C. Kühn, V. Lotoreichik, J. Rohleder)
Spectral theory for Schrödinger operators with δinteractions supported on curves in R^3.
Ann. H. Poincaré 18 (2017), no. 4, 1305  1347.
Article 
Preprint

(with E. H. Lieb, J. Sabin)
Maximizers for the SteinTomas inequality.
Geom. Funct. Anal. 26 (2016), no. 4, 1095  1134.
Article 
Preprint

Eigenvalue bounds for the fractional Laplacian: A review.
In: Recent Developments in Nonlocal Theory, G. Palatucci, T. Kuusi (eds.), 210  235, De Gruyter, 2017.
Article 
Preprint

(with R. Killip, P. T. Nam)
Nonexistence of large nuclei in the liquid drop model.
Lett. Math. Phys. 106 (2016), no. 8, 1033  1036.
Article 
Preprint

(with P. T. Nam, H. Van Den Bosch)
The ionization conjecture in ThomasFermiDiracvon Weizsäcker theory.
Comm. Pure Appl. Math. 71 (2018), no. 3, 577  614.
Article 
Preprint

(with E. H. Lieb)
A `liquidsolid' phase transition in a simple model for swarming.
Indiana Univ. Math. J., to appear.
Preprint

(with M. Lemm and B. Simon)
Condensation of fermion pairs in a domain.
Calc. Var. Partial Differential Equations 56 (2017), no. 2, 54.
Article 
Preprint

(with P. T. Nam, H. Van Den Bosch)
The maximal excess charge in Müller densitymatrixfunctional theory.
Ann. H. Poincaré, to appear.
Preprint

(with J. Sabin)
Spectral cluster bounds for orthonormal systems and oscillatory integral operators in Schatten spaces.
Adv. Math. 317 (2017), 157  192.
Article 
Preprint

(with J. Sabin)
The SteinTomas inequality in trace ideals.
Séminaire Laurent Schwartz  Équations aux dérivées partielles et applications. Année 2015  2016, Exp. No. XV, 12 pp., Ed. Éc. Polytech., Palaiseau, 2016.
Article 
Preprint

(with L. Schimmer)
Endpoint resolvent estimates for compact Riemannian manifolds.
J. Funct. Anal. 272 (2017), no. 9, 3904  3918.
Article 
Preprint

(with F. Méhats, C. Sparber)
Averaging of nonlinear Schrödinger equations with strong magnetic confinement.
Comm. Math. Sci. 15 (2017), no. 7, 1933  1945.
Article 
Preprint

(with E. H. Lieb)
Norms of quantum Gaussian multimode channels.
J. Math. Phys. 58 (2017), 062204.
Article 
Preprint

(with C. Hainzl, E. Langmann)
The BCS critical temperature in a weak homogeneous magnetic field.
J. Spectr. Theory, to appear.
Preprint

(with T. Jin, J. Xiong)
Minimizers for the fractional Sobolev inequality on domains.
Calc. Var. Partial Differential Equations 57 (2018), no. 2, 57  43.
Article 
Preprint

(with T. König)
Classification of positive solutions to a nonlinear biharmonic equation with critical exponent.
Anal. PDE, to appear.
Preprint

(with A. Laptev)
Bound on the number of negative eigenvalues of twodimensional Schrödinger operators on domains.
Algebra i Analiz, to appear.
Preprint

(with J. Sabin)
Extremizers for the AiryStrichartz inequality.
Math. Ann., to appear.
Article 
Preprint

(with J. Dolbeault, F. Hoffmann)
Reverse HardyLittlewoodSobolev inequalities.
Submitted.
Preprint
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Last modified: June 8, 2018