Frank, Rupert L.

Combined from CaltechAUTHORS

• Frank, Rupert L. (2023) Sharp inequalities for coherent states and their optimizers; Advanced Nonlinear Studies; Vol. 23; Art. No. 20220050; 10.1515/ans-2022-0050
• Frank, Rupert and Sukochev, Fedor, et el. (2023) Asymptotics of singular values for quantum derivatives; Transactions of the American Mathematical Society; Vol. 376; No. 3; 2047-2088; 10.1090/tran/8827
• Frank, Rupert L. and Merz, Konstantin, et el. (2023) The Scott conjecture for large Coulomb systems: a review; Letters in Mathematical Physics; Vol. 113; Art. No. 11; 10.1007/s11005-023-01631-9
• Frank, Rupert L. and Larson, Simon (2022) An inequality for the normal derivative of the Lane-Emden ground state; Advances in Calculus of Variations; 10.1515/acv-2022-0005
• Frank, Rupert L. (2022) Degenerate stability of some Sobolev inequalities; Analyse Nonlineaire, Annales Institute H. Poincaré; Vol. 39; No. 6; 1459-1484; 10.4171/aihpc/35
• Carrillo, J. A. and Delgadino, M. G., et el. (2022) Fast Diffusion leads to partial mass concentration in Keller–Segel type stationary solutions; Mathematical Models and Methods in Applied Sciences; Vol. 32; No. 4; 831-850; 10.1142/S021820252250018X
• Borichev, Alexander and Frank, Rupert L., et el. (2022) Counting eigenvalues of Schrödinger operators with fast decaying complex potentials; Advances in Mathematics; Vol. 397; Art. No. 108115; 10.1016/j.aim.2021.108115
• Frank, Rupert L. (2022) Minimizers for a one-dimensional interaction energy; Nonlinear Analysis; Vol. 216; Art. No. 112691; 10.1016/j.na.2021.112691
• Frank, Rupert L. and König, Tobias, et el. (2022) Reverse conformally invariant Sobolev inequalities on the sphere; Journal of Functional Analysis; Vol. 282; No. 4; Art. No. 109339; 10.1016/j.jfa.2021.109339
• Dolbeault, Jean and Frank, Rupert L., et el. (2022) Logarithmic estimates for mean-field models in dimension two and the Schrödinger–Poisson system; Comptes Rendus Mathématique; Vol. 359; No. 10; 1279-1293; 10.5802/crmath.272
• Frank, Rupert L. and Nam, Phan Thành (2021) Existence and nonexistence in the liquid drop model; Calculus of Variations and Partial Differential Equations; Vol. 60; No. 6; Art. No. 223; 10.1007/s00526-021-02072-9
• Frank, Rupert L. and Gontier, David, et el. (2021) Optimizers for the finite-rank Lieb-Thirring inequality; 10.48550/arXiv.2109.05984
• Frank, Rupert L. and Larson, Simon (2021) Discrete Schrödinger operators with decaying and oscillating potentials; 10.48550/arXiv.2108.05083
• Frank, Rupert L. (2021) Degenerate stability of some Sobolev inequalities; 10.48550/arXiv.2107.11608
• Frank, Rupert L. and Loss, Michael (2021) Existence of optimizers in a Sobolev inequality for vector fields; 10.48550/arXiv.2107.06450
• Frank, Rupert L. and Ivanisvili, Paata (2021) Hypercontractivity of the semigroup of the fractional Laplacian on the n-sphere; Journal of Functional Analysis; Vol. 281; No. 8; Art. No. 109145; 10.1016/j.jfa.2021.109145
• Frank, Rupert L. and König, Tobias, et el. (2021) Blow-up of solutions of critical elliptic equation in three dimensions; 10.48550/arXiv.2102.10525
• Frank, Rupert L. and Larson, Simon (2021) On the spectrum of the Kronig-Penney model in a constant electric field; 10.48550/arXiv.2104.10256
• Frank, Rupert L. and Merz, Konstantin, et el. (2021) Relativistic Strong Scott Conjecture: A Short Proof; 10.48550/arXiv.2009.02474
• Frank, Rupert L. and Gontier, David, et el. (2021) The periodic Lieb-Thirring inequality; 10.48550/arXiv.2010.02981
• Frank, Rupert L. and Loss, Michael (2021) Which magnetic fields support a zero mode?; Journal für die reine und angewandte Mathematik; 10.1515/crelle-2022-0015
• Frank, Rupert L. and Larson, Simon (2021) Semiclassical asymptotics for a class of singular Schrödinger operators; 10.48550/arXiv.2010.05417
• Frank, Rupert L. and Lieb, Elliott H. (2021) Proof of spherical flocking based on quantitative rearrangement inequalities; Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V; Vol. 22; No. 3; 1241-1263; 10.2422/2036-2145.201909_007
• Frank, Rupert L. (2021) Some minimization problems for mean field models with competing forces; 10.48550/arXiv.2109.02393
• Frank, Rupert L. and Hundertmark, Dirk, et el. (2021) The Lieb-Thirring inequality revisited; Journal of the European Mathematical Society; Vol. 23; No. 8; 2583-2600; 10.4171/jems/1062
• Frank, Rupert L. and Gontier, David, et el. (2021) The Nonlinear Schrödinger Equation for Orthonormal Functions II: Application to Lieb–Thirring Inequalities; Communications in Mathematical Physics; Vol. 384; No. 3; 1783-1828; 10.1007/s00220-021-04039-5
• Carlen, Eric A. and Frank, Rupert L., et el. (2021) Inequalities for Lᵖ-Norms that Sharpen the Triangle Inequality and Complement Hanner's Inequality; Journal of Geometric Analysis; Vol. 31; No. 4; 4051-4073; 10.1007/s12220-020-00425-y
• Frank, R. L. and Larson, S. (2021) Two Consequences of Davies' Hardy Inequality; Functional Analysis and Its Applications; Vol. 55; No. 2; 174-177; 10.1134/S0016266321020106
• Frank, Rupert L. and König, Tobias, et el. (2021) Energy asymptotics in the three-dimensional Brezis–Nirenberg problem; Calculus of Variations and Partial Differential Equations; Vol. 60; No. 2; Art. No. 58; 10.1007/s00526-021-01929-3
• Frank, Rupert L. and Seiringer, Robert (2021) Quantum Corrections to the Pekar Asymptotics of a Strongly Coupled Polaron; Communications on Pure and Applied Mathematics; Vol. 74; No. 3; 544-588; 10.1002/cpa.21944
• Frank, Rupert L. and Merz, Konstantin, et el. (2021) Equivalence of Sobolev Norms Involving Generalized Hardy Operators; International Mathematics Research Notices; Vol. 2021; No. 3; 2284-2303; 10.1093/imrn/rnz135
• Frank, Rupert L. and König, Tobias, et el. (2020) Classification of solutions of an equation related to a conformal log Sobolev inequality; Advances in Mathematics; Vol. 375; Art. No. 107395; 10.1016/j.aim.2020.107395
• Frank, Rupert L. and Kim, Seunghyeok, et el. (2020) Non-degeneracy for the critical Lane–Emden system; Proceedings of the American Mathematical Society; Vol. 149; No. 1; 265-278; 10.1090/proc/15217
• Frank, Rupert L. and Gang, Zhou (2020) A non-linear adiabatic theorem for the one-dimensional Landau–Pekar equations; Journal of Functional Analysis; Vol. 279; No. 7; Art. No. 108631; 10.1016/j.jfa.2020.108631
• Frank, Rupert L. and Larson, Simon (2020) Two-term spectral asymptotics for the Dirichlet Laplacian in a Lipschitz domain; Journal für die reine und angewandte Mathematik; Vol. 2020; No. 766; 195-228; 10.1515/crelle-2019-0019
• Frank, Rupert L. and Sabin, Julien (2020) Sharp Weyl laws with singular potentials; 10.48550/arXiv.2007.04284
• Frank, Rupert L. (2020) The Lieb-Thirring inequalities: Recent results and open problems; 10.48550/arXiv.2007.09326
• Carlen, Eric A. and Frank, Rupert L., et el. (2020) Inequalities that sharpen the triangle inequality for sums of N functions in L^p; Arkiv för Matematik; Vol. 58; No. 1; 57-69; 10.4310/ARKIV.2020.v58.n1.a4
• Emmert, Lukas and Frank, Rupert L., et el. (2020) Liquid Drop Model for Nuclear Matter in the Dilute Limit; SIAM Journal on Mathematical Analysis; Vol. 52; No. 2; 1980-1999; 10.1137/19M1274420
• Frank, Rupert L. and Larson, Simon (2020) On the error in the two-term Weyl formula for the Dirichlet Laplacian; Journal of Mathematical Physics; Vol. 61; No. 4; Art. No. 043504; 10.1063/1.5145003
• Borrelli, William and Frank, Rupert L. (2020) Sharp decay estimates for critical Dirac equations; Transactions of the American Mathematical Society; Vol. 373; No. 3; 2045-2070; 10.1090/tran/7958
• Frank, Rupert L. and Merz, Konstantin, et el. (2020) Proof of the Strong Scott Conjecture for Chandrasekhar Atoms; Pure and Applied Functional Analysis; Vol. 5; No. 6; 1319-1356; 10.48550/arXiv.1907.04894
• Carrillo, José A. and Delgadino, Matías G., et el. (2019) Reverse Hardy-Littlewood-Sobolev inequalities; Journal de Mathématiques Pures et Appliquées; Vol. 132; 133-165; 10.1016/j.matpur.2019.09.001
• Frank, Rupert L. and König, Tobias (2019) Singular solutions to a semilinear biharmonic equation with a general critical nonlinearity; Rendiconti Lincei - Matematica e Applicazioni; Vol. 30; No. 4; 817-846; 10.4171/RLM/871
• Frank, Rupert L. and Pushnitski, Alexander (2019) Schatten class conditions for functions of Schrödinger operators; Annales Henri Poincaré; Vol. 20; No. 11; 3543-3562; 10.1007/s00023-019-00838-8
• Frank, Rupert L. and Lieb, Elliott H. (2019) Periodic energy minimizers for a one-dimensional liquid drop model; Letters in Mathematical Physics; Vol. 109; No. 9; 2069-2081; 10.1007/s11005-019-01171-1
• Frank, Rupert L. and Pushnitski, Alexander (2019) Kato smoothness and functions of perturbed self-adjoint operators; Advances in Mathematics; Vol. 351; 343-387; 10.1016/j.aim.2019.05.002
• Frank, Rupert L. (2019) Non-spherical equilibrium shapes in the liquid drop model; Journal of Mathematical Physics; Vol. 60; No. 7; Art. No. 071506; 10.1063/1.5095603
• Carlen, Eric A. and Frank, Rupert L., et el. (2019) Inequalities for L^p-norms that sharpen the triangle inequality and complement Hanner's Inequality; 10.48550/arXiv.1807.05599
• Frank, R. L. and Laptev, A. (2019) Bound on the number of negative eigenvalues of two-dimensional Schrödinger operators on domains; ISBN 978-3-03719-175-0; Functional Analysis and Operator Theory for Quantum Physics: The Pavel Exner Anniversary Volume; St. Petersburg Mathematical Journal; Vol. 30; No. 3; 573-589; 10.1090/spmj/1559
• Frank, Rupert L. and König, Tobias (2019) Classification of positive singular solutions to a nonlinear biharmonic equation with critical exponent; Analysis & PDE; Vol. 12; No. 4; 1101-1113; 10.2140/apde.2019.12.1101
• Frank, Rupert L. and Hainzl, Christian, et el. (2019) The BCS critical temperature in a weak homogeneous magnetic field; Journal of Spectral Theory; Vol. 9; No. 3; 1005-1062; 10.4171/JST/270
• Frank, Rupert L. and Sabin, Julien (2018) Extremizers for the Airy–Strichartz inequality; Mathematische Annalen; Vol. 372; No. 3-4; 1121-1166; 10.1007/s00208-018-1695-7
• Carlen, Eric A. and Frank, Rupert L., et el. (2018) Inequalities for quantum divergences and the Audenaert–Datta conjecture; Journal of Physics A: Mathematical and Theoretical; Vol. 51; No. 48; Art. No. 483001; 10.1088/1751-8121/aae8a3
• Frank, Rupert L. and Hainzl, Christian (2018) The BCS Critical Temperature in a Weak External Electric Field via a Linear Two-Body Operator; ISBN 978-3-030-01601-2; Macroscopic Limits of Quantum Systems; 29-62; 10.1007/978-3-030-01602-9_2
• Frank, Rupert L. and Nam, Phan Thành, et el. (2018) A short proof of the ionization conjecture in Müller theory; ISBN 978-1-4704-3681-0; Mathematical Problems in Quantum Physics; 1-12; 10.1090/conm/717/14437
• Frank, Rupert L. and Nam, Phan Thành, et el. (2018) The Maximal Excess Charge in Müller Density-Matrix-Functional Theory; Annales Henri Poincaré; Vol. 19; No. 9; 2839-2867; 10.1007/s00023-018-0695-1
• Frank, Rupert L. and Jin, Tianling, et el. (2018) Minimizers for the fractional Sobolev inequality on domains; Calculus of Variations and Partial Differential Equations; Vol. 57; No. 2; Art. No. 43; 10.1007/s00526-018-1304-3
• Frank, Rupert L. and Nam, Phan Thành, et el. (2018) The ionization conjecture in Thomas-Fermi-Dirac-von Weizsäcker theory; Communications on Pure and Applied Mathematics; Vol. 71; No. 3; 577-614; 10.1002/cpa.21717
• Frank, Rupert L. and Lieb, Elliott H. (2018) A "Liquid-Solid" Phase Transition in a Simple Model for Swarming, Based on the "No Flat-Spots" Theorem for Subharmonic Functions; Indiana University Mathematics Journal; Vol. 67; No. 4; 1547-1569; 10.1512/iumj.2018.67.7398
• Frank, Rupert L. and Sabin, Julien (2017) Restriction theorems for orthonormal functions, Strichartz inequalities, and uniform Sobolev estimates; American Journal of Mathematics; Vol. 139; No. 6; 1649-1691; 10.1353/ajm.2017.0041
• Frank, Rupert L. and Simon, Barry (2017) Eigenvalue bounds for Schrödinger operators with complex potentials. II; Journal of Spectral Theory; Vol. 7; No. 3; 633-658; 10.4171/JST/173
• Frank, Rupert L. and Sabin, Julien (2017) Spectral cluster bounds for orthonormal systems and oscillatory integral operators in Schatten spaces; Advances in Mathematics; Vol. 317; 157-192; 10.1016/j.aim.2017.06.023
• Frank, Rupert L. (2017) Eigenvalue bounds for Schrödinger operators with complex potentials. III; Transactions of the American Mathematical Society; Vol. 370; 219-240; 10.1090/tran/6936
• Frank, Rupert L. and Lieb, Elliott H. (2017) Norms of quantum Gaussian multi-mode channels; Journal of Mathematical Physics; Vol. 58; No. 6; Art. No. 062204; 10.1063/1.4989809
• Frank, Rupert L. (2017) Remarks on eigenvalue estimates and semigroup domination; 10.48550/arXiv.0903.0561
• Frank, Rupert L. and Lenzmann, Enno (2017) Uniqueness of ground states for the L^2-critical boson star equation; 10.48550/arXiv.0905.3105
• Frank, Rupert L. and Lenzmann, Enno (2017) On ground states for the L^2-critical boson star equation; 10.48550/arXiv.0910.2721
• Frank, Rupert L. and Loss, Michael, et el. (2017) Pόlya's conjecture in the presence of a constant magnetic field; 10.48550/arXiv.0710.1078
• Frank, Rupert L. and Lieb, Elliott H., et el. (2017) Müeller's Exchange-Correlation Energy in Density-Matrix-Functional Theory; 10.48550/arXiv.0705.1587
• Frank, Rupert L. and Hansson, Anders (2017) Eigenvalue estimates for the Aharonov-Bohm operator in a domain; 10.48550/arXiv.0710.1089
• Ekholm, Tomas and Frank, Rupert L., et el. (2017) Remarks about Hardy inequalities on metric trees
• Frank, Rupert L. and Siedentop, Heinz, et el. (2017) The Energy of Heavy Atoms According to Brown and Ravenhall: The Scott Correction; 10.48550/arXiv.0805.4441
• Benguria, Rafael D. and Frank, Rupert L., et el. (2017) The sharp constant in the Hardy-Sobolev-Maz'ya inequality in the three dimensional upper half-space; 10.48550/arXiv.0705.3833
• Frank, Rupert L. and Laptev, Ari (2017) Spectral inequalities for Schrödinger operators with surface potentials; 10.48550/arXiv.0711.3473
• Frank, Rupert L. and Lieb, Elliott H., et el. (2017) Ground state properties of multi-polaron systems; 10.48550/arXiv.1209.3717
• Frank, R. L. and Hainzi, C., et el. (2017) Microscopic Derivation of the Ginzburg-Landau Model; 10.48550/arXiv.1209.1080
• Chen, Shibing and Frank, Rupert L., et el. (2017) Remainder terms in the fractional Sobolev inequality; 10.48550/arXiv.1205.5666
• Cornean, Horia D. and Fournais, Søren, et el. (2017) Sharp trace asymptotics for a class of 2D-magnetic operators; 10.48550/arXiv.1108.0777
• Dyda, Bartlomiej and Frank, Rupert L. (2017) Fractional Hardy-Sobolev-Maz'ya inequality for domains; 10.48550/arXiv.1109.6570
• Frank, Rupert L. and Lieb, Elliott H. (2017) Possible Lattice Distortions in the Hubbard Model for Graphene; 10.48550/arXiv.1105.0693
• Frank, Rupert L. and Lieb, Elliott H., et el. (2017) Binding of Polarons and Atoms at Threshold; 10.48550/arXiv.1106.0729
• Frank, Rupert L. and Schimmer, Lukas (2017) Endpoint resolvent estimates for compact Riemannian manifolds; Journal of Functional Analysis; Vol. 272; No. 9; 3904-3918; 10.1016/j.jfa.2016.11.012
• Frank, Rupert L. and Lenzmann, Enno (2017) Uniqueness and Nondegeneracy of Ground States for (−Δ)^sQ+Q−Q^(α+1)=0 in R; 10.48550/arXiv.1009.4042
• Frank, Rupert L. (2017) Eigenvalues of Schrödinger operators with complex surface potentials; ISBN 978-3-03719-175-0; Functional Analysis and Operator Theory for Quantum Physics: The Pavel Exner Anniversary Volume; 245-259; 10.4171/175
• Frank, Rupert L. and Lieb, Elliott H. (2017) A 'liquid-solid' phase transition in a simple model for swarming, based on the 'no flat-spots' theorem for subharmonic functions; 10.48550/arXiv.1607.07971
• Frank, Rupert L. and Lemm, Marius, et el. (2017) Condensation of fermion pairs in a domain; Calculus of Variations and Partial Differential Equations; Vol. 56; Art. No. 54; 10.1007/s00526-017-1140-x
• Behrndt, Jussi and Frank, Rupert L., et el. (2017) Spectral Theory for Schrödinger Operators with δ-Interactions Supported on Curves in R³; Annales Henri Poincaré; Vol. 18; No. 4; 1305-1347; 10.1007/s00023-016-0532-3
• Frank, Rupert L. (2017) Eigenvalue bounds for the fractional Laplacian: A review; ISBN 9783110571561; Recent Developments in Nonlocal Theory; 210-235; 10.1515/9783110571561-007
• Frank, Rupert L. and Méhats, Florian, et el. (2017) Averaging of nonlinear Schrödinger equations with strong magnetic confinement; Communications in Mathematical Sciences; Vol. 15; No. 7; 1933-1945; 10.4310/CMS.2017.v15.n7.a7
• Frank, Rupert L. and Zhou, Gang (2017) Derivation of an effective evolution equation for a strongly coupled polaron; Analysis & PDE; Vol. 10; No. 2; 379-422; 10.2140/apde.2017.10.379
• Frank, Rupert L. and Laptev, Ari, et el. (2016) On the number of eigenvalues of Schrödinger operators with complex potentials; Journal of the London Mathematical Society; Vol. 94; No. 2; 377-390; 10.1112/jlms/jdw039
• Frank, Rupert L. and Lemm, Marius (2016) Multi-Component Ginzburg-Landau Theory: Microscopic Derivation and Examples; Annales Henri Poincaré; Vol. 17; No. 9; 2285-2340; 10.1007/s00023-016-0473-x
• Frank, Rupert L. and Lenzmann, Enno, et el. (2016) Uniqueness of Radial Solutions for the Fractional Laplacian; Communications on Pure and Applied Mathematics; Vol. 69; No. 9; 1671-1726; 10.1002/cpa.21591
• Frank, Rupert L. and Killip, Rowan, et el. (2016) Nonexistence of Large Nuclei in the Liquid Drop Model; Letters in Mathematical Physics; Vol. 106; No. 8; 1033-1036; 10.1007/s11005-016-0860-8
• Frank, Rupert L. and Lieb, Elliott H., et el. (2016) Maximizers for the Stein–Tomas Inequality; Geometric and Functional Analysis; Vol. 26; No. 4; 1095-1134; 10.1007/s00039-016-0380-9
• Frank, Rupert L. and Hainzl, Christian, et el. (2016) Incompatibility of Time-Dependent Bogoliubov–de-Gennes and Ginzburg–Landau Equations; Letters in Mathematical Physics; Vol. 106; No. 7; 913-923; 10.1007/s11005-016-0847-5
• Frank, Rupert L. and Geisinger, Leander (2016) Refined semiclassical asymptotics for fractional powers of the Laplace operator; Journal für die reine und angewandte Mathematik; Vol. 2016; No. 712; 1-37; 10.1515/crelle-2013-0120
• Carlen, Eric A. and Frank, Rupert L., et el. (2016) Some operator and trace function convexity theorems; Linear Algebra and its Applications; Vol. 490; 174-185; 10.1016/j.laa.2015.11.006
• Frank, Rupert L. and Hainzl, Christian, et el. (2016) The External Field Dependence of the BCS Critical Temperature; Communications in Mathematical Physics; Vol. 342; No. 1; 189-216; 10.1007/s00220-015-2526-2
• Frank, Rupert L. and Sabin, Julien (2016) The Stein-Tomas inequality in trace ideals; Séminaire Laurent Schwartz - EDP et applications; Vol. 15; Art. No. 12; 10.5802/slsedp.92
• Frank, Rupert L. and Lieb, Elliott H. (2015) A Compactness Lemma and Its Application to the Existence of Minimizers for the Liquid Drop Model; SIAM Journal on Mathematical Analysis; Vol. 47; No. 6; 4436-4450; 10.1137/15M1010658
• Frank, Rupert L. and Geisinger, Leander (2015) The Ground State Energy of a Polaron in a Strong Magnetic Field; Communications in Mathematical Physics; Vol. 338; No. 1; 1-29; 10.1007/s00220-015-2367-z
• Ekholm, Tomas and Frank, Rupert L., et el. (2015) Weak perturbations of the p-Laplacian; Calculus of Variations and Partial Differential Equations; Vol. 53; No. 3-4; 781-801; 10.1007/s00526-014-0767-0
• Frank, Rupert L. and Pushnitski, Alexander (2015) The spectral density of a product of spectral projections; Journal of Functional Analysis; Vol. 268; No. 12; 3867-3894; 10.1016/j.jfa.2015.03.018
• Frank, Rupert L. and Pushnitski, Alexander (2015) Trace Class Conditions for Functions of Schrödinger Operators; Communications in Mathematical Physics; Vol. 335; No. 1; 477-496; 10.1007/s00220-014-2205-8
• Bengurla, Rafael D. and Frank, Rupert L., et el. (2015) Ground state energy of large polaron systems; Journal of Mathematical Physics; Vol. 56; No. 2; Art. No. 021901; 10.1063/1.4908125
• Frank, Rupert L. and González, María del Mar, et el. (2015) An extension problem for the CR fractional Laplacian; Advances in Mathematics; Vol. 270; 97-137; 10.1016/j.aim.2014.09.026
• Bellazzini, Jacopo and Frank, Rupert L., et el. (2014) Maximizers for Gagliardo–Nirenberg inequalities and related non-local problems; Mathematische Annalen; Vol. 360; No. 3-4; 653-673; 10.1007/s00208-014-1046-2
• Frank, Rupert L. and Schlein, Benjamin (2014) Dynamics of a Strongly Coupled Polaron; Letters in Mathematical Physics; Vol. 104; No. 8; 911-929; 10.1007/s11005-014-0700-7
• Frank, Rupert L. and Lewin, Mathieu, et el. (2014) Strichartz inequality for orthonormal functions; Journal of the European Mathematical Society; Vol. 16; No. 7; 1507-1526; 10.4171/JEMS/467
• Frank, Rupert L. and Lenz, Daniel, et el. (2014) Intrinsic metrics for non-local symmetric Dirichlet forms and applications to spectral theory; Journal of Functional Analysis; Vol. 266; No. 8; 4765-4808; 10.1016/j.jfa.2014.02.008
• Bellazzini, Jacopo and Frank, Rupert L., et el. (2014) Existence of ground states for negative ions at the binding threshold; Reviews in Mathematical Physics; Vol. 26; No. 01; Art. No. 1350021; 10.1142/S0129055X13500219
• Carlen, Eric A. and Frank, Rupert L., et el. (2014) Stability Estimates for the Lowest Eigenvalue of a Schrödinger Operator; Geometric and Functional Analysis; Vol. 24; No. 1; 63-84; 10.1007/s00039-014-0253-z
• Frank, Rupert L. (2014) Cwikel's theorem and the CLR inequality; Journal of Spectral Theory; Vol. 4; No. 1; 1-21; 10.4171/JST/59
• Frank, Rupert L. and Lieb, Elliott H. (2013) Monotonicity of a relative Rényi entropy; Journal of Mathematical Physics; Vol. 54; No. 12; Art. No. 122201; 10.1063/1.4838835
• Frank, Rupert L. and Lieb, Elliott H. (2013) Extended Quantum Conditional Entropy and Quantum Uncertainty Inequalities; Communications in Mathematical Physics; Vol. 323; No. 2; 487-495; 10.1007/s00220-013-1775-1
• Frank, Rupert L. and Lenzmann, Enno (2013) Uniqueness of non-linear ground states for fractional Laplacians in R; Acta Mathematica; Vol. 210; No. 2; 261-318; 10.1007/s11511-013-0095-9
• Frank, Rupert L. and Kovařík, Hynek (2013) Heat kernels of metric trees and applications; SIAM Journal on Mathematical Analysis; Vol. 45; No. 3; 1027-1046; 10.1137/120886297
• Frank, Rupert L. and Lieb, Elliott H., et el. (2013) Symmetry of Bipolaron Bound States for Small Coulomb Repulsion; Communications in Mathematical Physics; Vol. 319; No. 2; 557-573; 10.1007/s00220-012-1604-y
• Frank, Rupert L. and Lewin, Mathieu, et el. (2013) A positive density analogue of the Lieb–Thirring inequality; Duke Mathematical Journal; Vol. 162; No. 3; 435-495; 10.1215/00127094-2019477
• Frank, Rupert L. and Hainzl, Christian, et el. (2013) Derivation of Ginzburg-Landau theory for a one-dimensional system with contact interaction; ISBN 978-3-0348-0531-5; Operator Methods in Mathematical Physics; 57-88; 10.1007/978-3-0348-0531-5_3
• Frank, Rupert L. and Geisinger, Leander (2012) Semi-classical analysis of the Laplace operator with Robin boundary conditions; Bulletin of Mathematical Sciences; Vol. 2; No. 2; 281-319; 10.1007/s13373-012-0028-5
• Frank, Rupert L. and Lieb, Elliott H. (2012) Entropy and the Uncertainty Principle; Annales Henri Poincaré; Vol. 13; No. 8; 1711-1717; 10.1007/s00023-012-0175-y
• Frank, Rupert L. and Seiringer, Robert (2012) Lieb-Thirring inequality for a model of particles with point interactions; Journal of Mathematical Physics; Vol. 53; No. 9; Art. No. 095201; 10.1063/1.3697416
• Frank, Rupert L. and Hainzl, Christian, et el. (2012) Microscopic Derivation of Ginzburg-Landau Theory; Journal of the American Mathematical Society; Vol. 25; No. 3; 667-713; 10.1090/S0894-0347-2012-00735-8
• Frank, Rupert L. and Lieb, Elliott H. (2012) Sharp constants in several inequalities on the Heisenberg group; Annals of Mathematics; Vol. 176; No. 1; 349-381; 10.4007/annals.2012.176.1.6
• Frank, Rupert L. and Loss, Michael (2012) Hardy-Sobolev-Maz'ya inequalities for arbitrary domains; Journal de Mathématiques Pures et Appliquées; Vol. 97; No. 1; 39-54; 10.1016/j.matpur.2011.04.004
• Frank, Rupert L. and Lieb, Elliott H. (2012) A new, rearrangement-free proof of the sharp Hardy-Littlewood-Sobolev inequality; ISBN 978-3-0348-0263-5; Spectral Theory, Function Spaces and Inequalities; 55-67; 10.1007/978-3-0348-0263-5_4
• Frank, Rupert L. and Olofsson, Rikard (2011) Eigenvalue bounds for Schrödinger operators with a homogeneous magnetic field; Letters in Mathematical Physics; Vol. 97; 227-241; 10.1007/s11005-011-0499-4
• Frank, Rupert L. (2011) Eigenvalue bounds for Schrödinger operators with complex potentials; Bulletin of the London Mathematical Society; Vol. 43; No. 4; 745-750; 10.1112/blms/bdr008
• Frank, Rupert L. and Lieb, Elliott H., et el. (2011) Stability and Absence of Binding for Multi-Polaron Systems; Publications mathématiques de l'IHÉS; Vol. 113; No. 1; 39-67; 10.1007/s10240-011-0031-5
• Frank, Rupert L. and Lewin, Mathieu, et el. (2011) Energy Cost to Make a Hole in the Fermi Sea; Physical Review Letters; Vol. 106; No. 15; Art. No. 150402; 10.1103/PhysRevLett.106.150402
• Frank, Rupert L. and Simon, Barry (2011) Critical Lieb-Thirring bounds in gaps and the generalized Nevai conjecture for finite gap Jacobi matrices; Duke Mathematical Journal; Vol. 157; No. 3; 461-493; 10.1215/00127094-1272912
• Ekholm, Tomas and Frank, Rupert L., et el. (2011) Eigenvalue estimates for Schrödinger operators on metric trees; Advances in Mathematics; Vol. 226; No. 6; 5165-5197; 10.1016/j.aim.2011.01.001
• Frank, Rupert L. and Laptev, Ari, et el. (2011) A sharp bound on eigenvalues of Schröedinger operators on the half-line with complex-valued potentials; ISBN 9783764399948; Spectral Theory and Analysis; 39-44; 10.1007/978-3-7643-9994-8_3
• Frank, Rupert L. and Morozov, Sergey, et el. (2011) Weakly coupled bound states of Pauli operators; Calculus of Variations and Partial Differential Equations; Vol. 40; No. 1; 253-271; 10.1007/s00526-010-0339-x
• Frank, Rupert L. and Lieb, Elliott H., et el. (2011) Binding, Stability, and Non-binding of Multi-polaron Systems; ISBN 9789814350365; Mathematical Results in Quantum Physics; 21-32; 10.1142/9789814350365_0002
• Frank, Rupert L. and Geisinger, Leander (2011) Two-term spectral asymptotics for the Dirichlet Laplacian on a bounded domain; ISBN 9789814350365; Mathematical Results in Quantum Physics; 138-147; 10.1142/9789814350365_0012
• Frank, Rupert L. (2011) On the uniqueness of ground states of non-local equations; Journées équations aux dérivées partielles; Vol. 2011; A5; 10.5802/jedp.77
• Frank, Rupert L. and Lieb, Elliott H. (2011) Spherical reflection positivity and the Hardy-Littlewood-Sobolev inequality; ISBN 978-0-8218-4971-2; Concentration, Functional Inequalities and Isoperimetry; 89-102; 10.48550/arXiv.1003.5248
• Frank, Rupert L. and Lieb, Elliott H. (2010) Inversion positivity and the sharp Hardy–Littlewood–Sobolev inequality; Calculus of Variations and Partial Differential Equations; Vol. 39; No. 1-2; 85-99; 10.1007/s00526-009-0302-x
• Frank, Rupert L. and Lieb, Elliott H., et el. (2010) Bipolaron and N-Polaron Binding Energies; Physical Review Letters; Vol. 104; No. 21; Art. No. 210402; 10.1103/PhysRevLett.104.210402
• Frank, Rupert L. and Lieb, Elliott H., et el. (2010) Equivalence of Sobolev inequalities and Lieb-Thirring inequalities; ISBN 978-981-4304-62-7; XVIth International Congress on Mathematical Physics; 523-535; 10.1142/9789814304634_0045
• Frank, Rupert L. and Laptev, Ari (2010) Inequalities between Dirichlet and Neumann eigenvalues on the Heisenberg group; International Mathematics Research Notices; Vol. 2010; No. 15; 2889-2902; 10.1093/imrn/rnp230
• Frank, Rupert L. and Seiringer, Robert (2010) Sharp Fractional Hardy Inequalities in Half-Spaces; ISBN 978-1-4419-1340-1; Around the Research of Vladimir Maz'ya I; 161-167; 10.1007/978-1-4419-1341-8_6
• Frank, Rupert L. (2009) A Simple Proof of Hardy-Lieb-Thirring Inequalities; Communications in Mathematical Physics; Vol. 290; No. 2; 789-800; 10.1007/s00220-009-0759-7
• Breuer, Jonathan and Frank, Rupert L. (2009) Singular spectrum for radial trees; Reviews in Mathematical Physics; Vol. 21; No. 7; 929-945; 10.1142/S0129055X09003773
• Frank, Rupert L. (2009) A note on low energy scattering for homogeneous long range potentials; Annales Henri Poincaré; Vol. 10; No. 3; 573-575; 10.1007/s00023-009-0410-3
• Frank, Rupert L. and Seiringer, Robert (2008) Non-linear ground state representations and sharp Hardy inequalities; Journal of Functional Analysis; Vol. 255; No. 12; 3407-3430; 10.1016/j.jfa.2008.05.015
• Frank, Rupert L. and Simon, Barry, et el. (2008) Eigenvalue Bounds for Perturbations of Schrödinger Operators and Jacobi Matrices With Regular Ground States; Communications in Mathematical Physics; Vol. 282; No. 1; 199-208; 10.1007/s00220-008-0453-1
• Frank, Rupert L. and Siedentop, Heinz, et el. (2008) The Ground State Energy of Heavy Atoms: Relativistic Lowering of the Leading Energy Correction; Communications in Mathematical Physics; Vol. 278; No. 2; 549-566; 10.1007/s00220-007-0397-x
• Ekholm, Tomas and Frank, Rupert (2008) Lieb–Thirring inequalities on the half-line with critical exponent; European Mathematical Society; Vol. 10; No. 3; 739-755; 10.4171/JEMS/128
• Frank, Rupert L. and Lieb, Elliott H., et el. (2007) Number of Bound States of Schröedinger Operators with Matrix-Valued Potentials; Letters in Mathematical Physics; Vol. 82; No. 2-3; 107-116; 10.1007/s11005-007-0211-x
• Frank, Rupert L. and Hainzl, Christian, et el. (2007) The critical temperature for the BCS equation at weak coupling; Journal of Geometric Analysis; Vol. 17; No. 4; 559-567; 10.1007/BF02937429
• Frank, Rupert L. and Laptev, Ari, et el. (2007) Eigenvalue estimates for magnetic Schrödinger operators in domains; Proceedings of the American Mathematical Society; Vol. 136; No. 12; 4245-4255; 10.1090/S0002-9939-08-09523-3
• Frank, Rupert L. and Lieb, Elliott H., et el. (2007) Hardy-Lieb-Thirring inequalities for fractional Schrödinger operators; Journal of the American Mathematical Society; Vol. 21; No. 4; 925-950; 10.1090/S0894-0347-07-00582-6
• Frank, Rupert L. and Lieb, Elliott H., et el. (2007) Stability of Relativistic Matter with Magnetic Fields for Nuclear Charges up to the Critical Value; Communications in Mathematical Physics; Vol. 275; No. 2; 479-489; 10.1007/s00220-007-0307-2
• Frank, Rupert L. (2007) On the asymptotic number of edge states for magnetic Schrödinger operators; Proceedings of the London Mathematical Society; Vol. 95; No. 1; 1-19; 10.1112/plms/pdl024
• Exner, Pavel and Frank, Rupert L. (2007) Absolute Continuity of the Spectrum for Periodically Modulated Leaky Wires in R^3; Annales Henri Poincaré; Vol. 8; No. 2; 241-263; 10.1007/s00023-006-0307-3
• Frank, Rupert L. and Laptev, Ari, et el. (2006) Lieb–Thirring Inequalities for Schrödinger Operators with Complex-valued Potentials; Letters in Mathematical Physics; Vol. 77; No. 3; 309-316; 10.1007/s11005-006-0095-1