Edit Profile (opens in new tab) Frank, Rupert L. Compute Distance To: Compute Author ID: frank.rupert-l Published as: Frank, Rupert L.; Frank, R. L.; Frank, Rupert more...less External Links: MGP Documents Indexed: 143 Publications since 2003 1 Contribution as Editor Co-Authors: 82 Co-Authors with 128 Joint Publications 2,197 Co-Co-Authors all top 5 Co-Authors 14 single-authored 32 Lieb, Elliott H. 24 Seiringer, Robert 8 Hainzl, Christian 7 Laptev, Ari 6 König, Tobias 6 Phan Thành Nam 5 Carlen, Eric Anders 5 Ekholm, Tomas 5 Kovařík, Hynek 5 Lewin, Mathieu 5 Sabin, Julien 5 Simon, Barry 4 Geisinger, Leander 4 Loss, Michael 4 Pushnitski, Alexander B. 4 Siedentop, Heinz Karl Heinrich 4 Solovej, Jan Philip 3 Larson, Simon 3 Thomas, Lawrence E. 3 Van Den Bosch, Hanne 3 Weidl, Timo 2 Bellazzini, Jacopo 2 Benguria, Rafael D. 2 Carrillo de la Plata, José Antonio 2 Delgadino, Matias Gonzalo 2 Dolbeault, Jean 2 Exner, Pavel 2 Gontier, David 2 Ivanisvili, Paata 2 Lemm, Marius 2 Lenzmann, Enno 2 Merz, Konstantin 2 Schlein, Benjamin 2 Shterenberg, Roman G. 2 Tang, Hanli 2 Warzel, Simone 1 Behrndt, Jussi 1 Borichev, Aleksandr Aleksandrovich 1 Borrelli, William 1 Breuer, Jonathan 1 Chen, Shibing 1 Cornean, Horia D. 1 Dyda, Bartłomiej 1 Emmert, Lukas 1 Fournais, Søren 1 Gang, Zhou 1 Gesztesy, Fritz 1 González, María del Mar 1 Hansson, Anders M. 1 Helffer, Bernard 1 Hoffmann, Franca 1 Holden, Helge 1 Hundertmark, Dirk 1 Jeanjean, Louis 1 Jex, Michal 1 Jin, Tianling 1 Killip, Rowan 1 Kim, Seunghyeok 1 Kühn, Christian 1 Langmann, Edwin 1 Lenz, Daniel H. 1 Lotoreichik, Vladimir 1 Méhats, Florian 1 Molchanov, Stanislav Alekseevich 1 Monticelli, Dario Daniele 1 Morozov, Sergey 1 Naboko, Serguei N. 1 Olofsson, Rikard 1 Pistoia, Angela 1 Rohleder, Jonathan 1 Safronov, Oleg 1 Schimmer, Lukas 1 Silvestre, Luis E. 1 Sparber, Christof 1 Tan, Jinggang 1 Visciglia, Nicola 1 Volberg, Alexander Lvovich 1 Vugal’ter, Semën Abramovich 1 Weth, Tobias 1 Wingert, Daniel 1 Xiong, Jingang 1 Zhou, Gang all top 5 Serials 12 Communications in Mathematical Physics 7 Letters in Mathematical Physics 7 Journal of Functional Analysis 7 Calculus of Variations and Partial Differential Equations 7 Annales Henri Poincaré 6 Journal of Mathematical Physics 6 Advances in Mathematics 4 Journal of the European Mathematical Society (JEMS) 3 Communications on Pure and Applied Mathematics 3 Journal für die Reine und Angewandte Mathematik 3 IMRN. International Mathematics Research Notices 3 SIAM Journal on Mathematical Analysis 3 Documenta Mathematica 3 Journal of Spectral Theory 2 Arkiv för Matematik 2 Reviews in Mathematical Physics 2 Duke Mathematical Journal 2 Indiana University Mathematics Journal 2 Mathematische Annalen 2 Proceedings of the American Mathematical Society 2 Transactions of the American Mathematical Society 2 Journal of the American Mathematical Society 2 The Journal of Geometric Analysis 2 Geometric and Functional Analysis. GAFA 2 Journal de Mathématiques Pures et Appliquées. Neuvième Série 2 Analysis & PDE 1 Studia Mathematica 1 Acta Mathematica 1 American Journal of Mathematics 1 Annales de l’Institut Fourier 1 Bulletin of the London Mathematical Society 1 Functional Analysis and its Applications 1 Publications Mathématiques 1 Journal of the London Mathematical Society. Second Series 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Proceedings of the London Mathematical Society. Third Series 1 Asymptotic Analysis 1 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni 1 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 1 Linear Algebra and its Applications 1 St. Petersburg Mathematical Journal 1 Mathematical Research Letters 1 Annals of Mathematics. Second Series 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Communications in Mathematical Sciences 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 1 Journal of Physics A: Mathematical and Theoretical 1 Bulletin of Mathematical Sciences 1 Séminaire Laurent Schwartz. EDP et Applications 1 Pure and Applied Functional Analysis 1 EMS Series of Congress Reports all top 5 Fields 83 Partial differential equations (35-XX) 57 Quantum theory (81-XX) 29 Operator theory (47-XX) 25 Functional analysis (46-XX) 23 Statistical mechanics, structure of matter (82-XX) 18 Real functions (26-XX) 13 Calculus of variations and optimal control; optimization (49-XX) 8 Harmonic analysis on Euclidean spaces (42-XX) 6 Potential theory (31-XX) 6 Difference and functional equations (39-XX) 6 Information and communication theory, circuits (94-XX) 5 Probability theory and stochastic processes (60-XX) 3 Ordinary differential equations (34-XX) 3 Global analysis, analysis on manifolds (58-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 1 General and overarching topics; collections (00-XX) 1 Combinatorics (05-XX) 1 Measure and integration (28-XX) 1 Functions of a complex variable (30-XX) 1 Optics, electromagnetic theory (78-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 126 Publications have been cited 2,088 times in 1,329 Documents Cited by ▼ Year ▼ Uniqueness of non-linear ground states for fractional Laplacians in \(\mathbb{R}\). Zbl 1307.35315Frank, Rupert L.; Lenzmann, Enno 182 2013 Uniqueness of radial solutions for the fractional Laplacian. Zbl 1365.35206Frank, Rupert L.; Lenzmann, Enno; Silvestre, Luis 178 2016 Nonlinear ground state representations and sharp Hardy inequalities. Zbl 1189.26031Frank, Rupert L.; Seiringer, Robert 153 2008 Hardy-Lieb-Thirring inequalities for fractional Schrödinger operators. Zbl 1202.35146Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert 133 2008 Sharp constants in several inequalities on the Heisenberg group. Zbl 1252.42023Frank, Rupert L.; Lieb, Elliott H. 70 2012 Monotonicity of a relative Rényi entropy. Zbl 1350.94020Frank, Rupert L.; Lieb, Elliott H. 57 2013 Eigenvalue bounds for Schrödinger operators with complex potentials. Zbl 1228.35158Frank, Rupert L. 54 2011 Inversion positivity and the sharp Hardy-Littlewood-Sobolev inequality. Zbl 1204.39024Frank, Rupert L.; Lieb, Elliott H. 51 2010 Intrinsic metrics for non-local symmetric Dirichlet forms and applications to spectral theory. Zbl 1304.60081Frank, Rupert L.; Lenz, Daniel; Wingert, Daniel 47 2014 Lieb-Thirring inequalities for Schrödinger operators with complex-valued potentials. Zbl 1160.81382Frank, Rupert L.; Laptev, Ari; Lieb, Elliott H.; Seiringer, Robert 44 2006 Maximizers for Gagliardo-Nirenberg inequalities and related non-local problems. Zbl 1320.46026Bellazzini, Jacopo; Frank, Rupert L.; Visciglia, Nicola 36 2014 A new, rearrangement-free proof of the sharp Hardy-Littlewood-Sobolev inequality. Zbl 1297.39023Frank, Rupert L.; Lieb, Elliott H. 36 2012 The sharp constant in the Hardy-Sobolev-Maz’ya inequality in the three-dimensional upper half space. Zbl 1173.26011Benguria, Rafael D.; Frank, Rupert L.; Loss, Michael 36 2008 Eigenvalue bounds for Schrödinger operators with complex potentials. III. Zbl 1390.35204Frank, Rupert L. 35 2018 Restriction theorems for orthonormal functions, Strichartz inequalities, and uniform Sobolev estimates. Zbl 1388.42018Frank, Rupert L.; Sabin, Julien 35 2017 A compactness lemma and its application to the existence of minimizers for the liquid drop model. Zbl 1332.49042Frank, Rupert L.; Lieb, Elliott H. 31 2015 Eigenvalue bounds for Schrödinger operators with complex potentials II. Zbl 1386.35061Frank, Rupert L.; Simon, Barry 28 2017 Microscopic derivation of Ginzburg-Landau theory. Zbl 1251.35156Frank, Rupert L.; Hainzl, Christian; Seiringer, Robert; Solovej, Jan Philip 28 2012 The critical temperature for the BCS equation at weak coupling. Zbl 1137.82025Frank, Rupert L.; Hainzl, Christian; Naboko, Serguei; Seiringer, Robert 28 2007 An extension problem for the CR fractional Laplacian. Zbl 1304.35747Frank, Rupert L.; del Mar González, María; Monticelli, Dario D.; Tan, Jinggang 27 2015 Refined semiclassical asymptotics for fractional powers of the Laplace operator. Zbl 1337.35163Frank, Rupert L.; Geisinger, Leander 27 2016 On Lieb-Thirring inequalities for Schrödinger operators with virtual level. Zbl 1106.81039Ekholm, T.; Frank, R. L. 26 2006 A simple proof of Hardy-Lieb-Thirring inequalities. Zbl 1184.35121Frank, Rupert L. 25 2009 On the number of eigenvalues of Schrödinger operators with complex potentials. Zbl 1358.35074Frank, Rupert L.; Laptev, Ari; Safronov, Oleg 24 2016 Remainder terms in the fractional Sobolev inequality. Zbl 1296.46032Chen, Shibing; Frank, Rupert L.; Weth, Tobias 23 2013 Strichartz inequality for orthonormal functions. Zbl 1307.35245Frank, Rupert L.; Lewin, Mathieu; Lieb, Elliott H.; Seiringer, Robert 22 2014 Sharp fractional Hardy inequalities in half-spaces. Zbl 1185.26044Frank, Rupert L.; Seiringer, Robert 21 2010 Stability estimates for the lowest eigenvalue of a Schrödinger operator. Zbl 1291.35145Carlen, Eric A.; Frank, Rupert L.; Lieb, Elliott H. 20 2014 A positive density analogue of the Lieb-Thirring inequality. Zbl 1260.35088Frank, Rupert L.; Lewin, Mathieu; Lieb, Elliott H.; Seiringer, Robert 19 2013 Hardy-Sobolev-Maz’ya inequalities for arbitrary domains. Zbl 1233.49023Frank, Rupert L.; Loss, Michael 17 2012 Fractional Hardy-Sobolev-Maz’ya inequality for domains. Zbl 1273.26025Dyda, Bartłomiej; Frank, Rupert L. 17 2012 Classification of positive singular solutions to a nonlinear biharmonic equation with critical exponent. Zbl 1421.35150Frank, Rupert L.; König, Tobias 16 2019 Derivation of an effective evolution equation for a strongly coupled polaron. Zbl 1365.35130Frank, Rupert L.; Zhou, Gang 16 2017 Singular spectrum for radial trees. Zbl 1177.05069Breuer, Jonathan; Frank, Rupert L. 16 2009 A sharp bound on eigenvalues of Schrödinger operators on the half-line with complex-valued potentials. Zbl 1253.35086Frank, Rupert L.; Laptev, Ari; Seiringer, Robert 15 2011 Nonexistence of large nuclei in the liquid drop model. Zbl 1347.49069Frank, Rupert L.; Killip, Rowan; Phan Thành Nam 15 2016 The ionization conjecture in Thomas-Fermi-Dirac-von Weizsäcker theory. Zbl 1386.49063Frank, Rupert L.; Phan Thành Nam; Van Den Bosch, Hanne 15 2018 Eigenvalue bounds for perturbations of Schrödinger operators and Jacobi matrices with regular ground states. Zbl 1158.35021Frank, Rupert L.; Simon, Barry; Weidl, Timo 14 2008 Lieb-Thirring inequality for a model of particles with point interactions. Zbl 1278.81061Frank, Rupert L.; Seiringer, Robert 13 2012 Cwikel’s theorem and the CLR inequality. Zbl 1295.35347Frank, Rupert L. 13 2014 Dynamics of a strongly coupled polaron. Zbl 1297.35202Frank, Rupert L.; Schlein, Benjamin 13 2014 Maximizers for the Stein-Tomas inequality. Zbl 1357.42023Frank, Rupert L.; Lieb, Elliott H.; Sabin, Julien 13 2016 Stability and absence of binding for multi-polaron systems. Zbl 1227.82083Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert; Thomas, Lawrence E. 13 2011 Pólya’s conjecture in the presence of a constant magnetic field. Zbl 1179.35205Frank, Rupert L.; Loss, Michael; Weidl, Timo 13 2009 A “liquid-solid” phase transition in a simple model for swarming, based on the “no flat-spots” theorem for subharmonic functions. Zbl 1420.49040Frank, Rupert; Lieb, Elliott H. 12 2018 Stability of relativistic matter with magnetic fields for nuclear charges up to the critical value. Zbl 1135.81030Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert 12 2007 The ground state energy of heavy atoms: Relativistic lowering of the leading energy correction. Zbl 1162.81037Frank, Rupert L.; Siedentop, Heinz; Warzel, Simone 11 2008 Some operator and trace function convexity theorems. Zbl 1342.47024Carlen, Eric A.; Frank, Rupert L.; Lieb, Elliott H. 11 2016 Equivalence of Sobolev inequalities and Lieb-Thirring inequalities. Zbl 1203.81072Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert 10 2010 Inequalities for quantum divergences and the Audenaert-Datta conjecture. Zbl 1414.81064Carlen, Eric A.; Frank, Rupert L.; Lieb, Elliott H. 9 2018 Sharp decay estimates for critical Dirac equations. Zbl 1435.35053Borrelli, William; Frank, Rupert L. 9 2020 On the asymptotic number of edge states for magnetic Schrödinger operators. Zbl 1131.35076Frank, Rupert L. 9 2007 Binding of polarons and atoms at threshold. Zbl 1250.82046Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert 9 2012 Eigenvalue estimates for Schrödinger operators on metric trees. Zbl 1237.35157Ekholm, Tomas; Frank, Rupert L.; Kovařík, Hynek 9 2011 Critical Lieb-Thirring bounds in gaps and the generalized Nevai conjecture for finite gap Jacobi matrices. Zbl 1229.35157Frank, Rupert L.; Simon, Barry 9 2011 The energy of heavy atoms according to Brown and Ravenhall: the Scott correction. Zbl 1186.81137Frank, Rupert L.; Siedentop, Heinz; Warzel, Simone 9 2009 Eigenvalue bounds for the fractional Laplacian: a review. Zbl 1404.35303Frank, Rupert L. 8 2018 Two-term spectral asymptotics for the Dirichlet Laplacian on a bounded domain. Zbl 1253.47031Frank, Rupert L.; Geisinger, Leander 8 2011 The external field dependence of the BCS critical temperature. Zbl 1334.82080Frank, Rupert L.; Hainzl, Christian; Seiringer, Robert; Solovej, Jan Philip 8 2016 Semi-classical analysis of the Laplace operator with Robin boundary conditions. Zbl 1253.35090Frank, Rupert L.; Geisinger, Leander 8 2012 Extended quantum conditional entropy and quantum uncertainty inequalities. Zbl 1280.81022Frank, Rupert L.; Lieb, Elliott H. 7 2013 Minimizers for the fractional Sobolev inequality on domains. Zbl 1393.26026Frank, Rupert L.; Jin, Tianling; Xiong, Jingang 7 2018 Norms of quantum Gaussian multi-mode channels. Zbl 1366.81091Frank, Rupert L.; Lieb, Elliott H. 7 2017 Derivation of Ginzburg-Landau theory for a one-dimensional system with contact interaction. Zbl 1277.82073Frank, Rupert L.; Hainzl, Christian; Seiringer, Robert; Solovej, Jan Philip 6 2013 A non-linear adiabatic theorem for the one-dimensional Landau-Pekar equations. Zbl 1445.35128Frank, Rupert L.; Gang, Zhou 6 2020 Trace class conditions for functions of Schrödinger operators. Zbl 1310.47016Frank, Rupert L.; Pushnitski, Alexander 6 2015 The spectral density of a product of spectral projections. Zbl 1312.81071Frank, Rupert L.; Pushnitski, Alexander 6 2015 Multi-component Ginzburg-Landau theory: microscopic derivation and examples. Zbl 1351.82117Frank, Rupert L.; Lemm, Marius 6 2016 Spectral theory for Schrödinger operators with \(\delta\)-interactions supported on curves in \(\mathbb {R}^3\). Zbl 1378.81026Behrndt, Jussi; Frank, Rupert L.; Kühn, Christian; Lotoreichik, Vladimir; Rohleder, Jonathan 6 2017 Spectral inequalities for Schrödinger operators with surface potentials. Zbl 1170.35486Frank, Rupert L.; Laptev, Ari 6 2008 Lieb-Thirring inequalities on the half-line with critical exponent. Zbl 1147.35020Ekholm, Tomas; Frank, Rupert L. 5 2008 Eigenvalue estimates for magnetic Schrödinger operators in domains. Zbl 1186.35119Frank, Rupert L.; Laptev, Ari; Molchanov, Stanislav 5 2008 The maximal excess charge in Müller density-matrix-functional theory. Zbl 1397.81456Frank, Rupert L.; Phan Thành Nam; van den Bosch, Hanne 5 2018 Reverse Hardy-Littlewood-Sobolev inequalities. Zbl 1442.35011Carrillo, José A.; Delgadino, Matías G.; Dolbeault, Jean; Frank, Rupert L.; Hoffmann, Franca 5 2019 Sharp trace asymptotics for a class of \(2D\)-magnetic operators. (Asymptotiques précisées pour la trace d’une classe d’opérateurs de Schrödinger magnétiques en dimension 2.) Zbl 1301.35070Cornean, Horia D.; Fournais, Søren; Frank, Rupert L.; Helffer, Bernard 5 2013 Endpoint resolvent estimates for compact Riemannian manifolds. Zbl 1360.58015Frank, Rupert L.; Schimmer, Lukas 5 2017 Absolute continuity of the spectrum for periodically modulated leaky wires in \({\mathbb{R}^{3}}\). Zbl 1206.82112Exner, Pavel; Frank, Rupert L. 5 2007 Number of bound states of Schrödinger operators with matrix-valued potentials. Zbl 1135.35052Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert 5 2007 Spherical reflection positivity and the Hardy-Littlewood-Sobolev inequality. Zbl 1378.39013Frank, Rupert L.; Lieb, Elliott H. 5 2011 Weakly coupled bound states of Pauli operators. Zbl 1205.35177Frank, Rupert L.; Morozov, Sergey; Vugalter, Semjon 5 2011 On the scattering theory of the Laplacian with a periodic boundary condition. I. Existence of wave operators. Zbl 1142.35374Frank, Rupert L. 4 2003 Two-term spectral asymptotics for the Dirichlet Laplacian in a Lipschitz domain. Zbl 1467.35107Frank, Rupert L.; Larson, Simon 4 2020 Equivalence of Sobolev norms involving generalized Hardy operators. Zbl 1470.81033Frank, Rupert L.; Merz, Konstantin; Siedentop, Heinz 4 2021 Inequalities between Dirichlet and Neumann eigenvalues on the Heisenberg group. Zbl 1198.35161Frank, Rupert L.; Laptev, Ari 4 2010 Remarks on eigenvalue estimates and semigroup domination. Zbl 1183.81068Frank, Rupert L. 4 2009 Ground state properties of multi-polaron systems. Zbl 1304.82075Frank, R. L.; Lieb, E. H.; Seiringer, R.; Thomas, L. E. 4 2014 Entropy and the uncertainty principle. Zbl 1256.81022Frank, Rupert L.; Lieb, Elliott H. 4 2012 The ground state energy of a polaron in a strong magnetic field. Zbl 1323.82045Frank, Rupert L.; Geisinger, Leander 4 2015 Kato smoothness and functions of perturbed self-adjoint operators. Zbl 07078811Frank, Rupert L.; Pushnitski, Alexander 3 2019 Heat kernels of metric trees and applications. Zbl 1278.47048Frank, Rupert L.; Kovařík, Hynek 3 2013 Remarks about Hardy inequalities on metric trees. Zbl 1175.26035Ekholm, Tomas; Frank, Rupert L.; Kovařík, Hynek 3 2008 On the spectrum of partially periodic operators. Zbl 1210.35041Frank, Rupert L.; Shterenberg, Roman G. 3 2007 Classification of solutions of an equation related to a conformal log Sobolev inequality. Zbl 1453.35036Frank, Rupert L.; König, Tobias; Tang, Hanli 3 2020 Quantum corrections to the Pekar asymptotics of a strongly coupled polaron. Zbl 1467.82092Frank, Rupert L.; Seiringer, Robert 3 2021 Existence of ground states for negative ions at the binding threshold. Zbl 1302.81099Bellazzini, Jacopo; Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert 3 2014 On the scattering theory of the Laplacian with a periodic boundary condition. II. Additional channels of scattering. Zbl 1210.35040Frank, Rupert L.; Shterenberg, Roman G. 3 2004 Spectral cluster bounds for orthonormal systems and oscillatory integral operators in Schatten spaces. Zbl 1373.58015Frank, Rupert L.; Sabin, Julien 3 2017 The Stein-Tomas inequality in trace ideals. Zbl 1358.35010Frank, Rupert L.; Sabin, Julien 3 2016 On the tunneling effect for magnetic Schrödinger operators in antidot lattices. Zbl 1157.81309Frank, Rupert L. 3 2006 Weak perturbations of the \(p\)-Laplacian. Zbl 1322.49076Ekholm, Tomas; Frank, Rupert L.; Kovařík, Hynek 3 2015 Counting eigenvalues of Schrödinger operators with fast decaying complex potentials. Zbl 07472307Borichev, Alexander; Frank, Rupert L.; Volberg, Alexander 1 2022 Equivalence of Sobolev norms involving generalized Hardy operators. Zbl 1470.81033Frank, Rupert L.; Merz, Konstantin; Siedentop, Heinz 4 2021 Quantum corrections to the Pekar asymptotics of a strongly coupled polaron. Zbl 1467.82092Frank, Rupert L.; Seiringer, Robert 3 2021 Existence and nonexistence in the liquid drop model. Zbl 07414044Frank, Rupert L.; Nam, Phan Thành 3 2021 The nonlinear Schrödinger equation for orthonormal functions. II: Application to Lieb-Thirring inequalities. Zbl 1465.35015Frank, Rupert L.; Gontier, David; Lewin, Mathieu 2 2021 The Lieb-Thirring inequality revisited. Zbl 1467.35014Frank, Rupert L.; Hundertmark, Dirk; Jex, Michal; Nam, Phan Thành 1 2021 Non-degeneracy for the critical Lane-Emden system. Zbl 1464.35097Frank, Rupert L.; Kim, Seunghyeok; Pistoia, Angela 1 2021 Proof of spherical flocking based on quantitative rearrangement inequalities. Zbl 1478.49020Frank, Rupert L.; Lieb, Elliott H. 1 2021 Sharp decay estimates for critical Dirac equations. Zbl 1435.35053Borrelli, William; Frank, Rupert L. 9 2020 A non-linear adiabatic theorem for the one-dimensional Landau-Pekar equations. Zbl 1445.35128Frank, Rupert L.; Gang, Zhou 6 2020 Two-term spectral asymptotics for the Dirichlet Laplacian in a Lipschitz domain. Zbl 1467.35107Frank, Rupert L.; Larson, Simon 4 2020 Classification of solutions of an equation related to a conformal log Sobolev inequality. Zbl 1453.35036Frank, Rupert L.; König, Tobias; Tang, Hanli 3 2020 Proof of the strong Scott conjecture for Chandrasekhar atoms. Zbl 1465.81076Frank, Rupert L.; Merz, Konstantin; Siedentop, Heinz; Simon, Barry 1 2020 Inequalities that sharpen the triangle inequality for sums of \(N\) functions in \(L^p\). Zbl 1479.46029Carlen, Eric A.; Frank, Rupert L.; Lieb, Elliott H. 1 2020 Liquid drop model for nuclear matter in the dilute limit. Zbl 1439.81090Emmert, Lukas; Frank, Rupert L.; König, Tobias 1 2020 On the error in the two-term Weyl formula for the Dirichlet Laplacian. Zbl 1458.35142Frank, Rupert L.; Larson, Simon 1 2020 Classification of positive singular solutions to a nonlinear biharmonic equation with critical exponent. Zbl 1421.35150Frank, Rupert L.; König, Tobias 16 2019 Reverse Hardy-Littlewood-Sobolev inequalities. Zbl 1442.35011Carrillo, José A.; Delgadino, Matías G.; Dolbeault, Jean; Frank, Rupert L.; Hoffmann, Franca 5 2019 Kato smoothness and functions of perturbed self-adjoint operators. Zbl 07078811Frank, Rupert L.; Pushnitski, Alexander 3 2019 Singular solutions to a semilinear biharmonic equation with a general critical nonlinearity. Zbl 1454.35102Frank, Rupert L.; König, Tobias 2 2019 Schatten class conditions for functions of Schrödinger operators. Zbl 07120692Frank, Rupert L.; Pushnitski, Alexander 2 2019 Periodic energy minimizers for a one-dimensional liquid drop model. Zbl 1428.82062Frank, Rupert L.; Lieb, Elliott H. 2 2019 Non-spherical equilibrium shapes in the liquid drop model. Zbl 1416.81223Frank, Rupert L. 1 2019 Eigenvalue bounds for Schrödinger operators with complex potentials. III. Zbl 1390.35204Frank, Rupert L. 35 2018 The ionization conjecture in Thomas-Fermi-Dirac-von Weizsäcker theory. Zbl 1386.49063Frank, Rupert L.; Phan Thành Nam; Van Den Bosch, Hanne 15 2018 A “liquid-solid” phase transition in a simple model for swarming, based on the “no flat-spots” theorem for subharmonic functions. Zbl 1420.49040Frank, Rupert; Lieb, Elliott H. 12 2018 Inequalities for quantum divergences and the Audenaert-Datta conjecture. Zbl 1414.81064Carlen, Eric A.; Frank, Rupert L.; Lieb, Elliott H. 9 2018 Eigenvalue bounds for the fractional Laplacian: a review. Zbl 1404.35303Frank, Rupert L. 8 2018 Minimizers for the fractional Sobolev inequality on domains. Zbl 1393.26026Frank, Rupert L.; Jin, Tianling; Xiong, Jingang 7 2018 The maximal excess charge in Müller density-matrix-functional theory. Zbl 1397.81456Frank, Rupert L.; Phan Thành Nam; van den Bosch, Hanne 5 2018 Extremizers for the Airy-Strichartz inequality. Zbl 1406.35354Frank, Rupert L.; Sabin, Julien 2 2018 A short proof of the ionization conjecture in Müller theory. Zbl 1423.81198Frank, Rupert L.; Phan Thành Nam; Van Den Bosch, Hanne 1 2018 Restriction theorems for orthonormal functions, Strichartz inequalities, and uniform Sobolev estimates. Zbl 1388.42018Frank, Rupert L.; Sabin, Julien 35 2017 Eigenvalue bounds for Schrödinger operators with complex potentials II. Zbl 1386.35061Frank, Rupert L.; Simon, Barry 28 2017 Derivation of an effective evolution equation for a strongly coupled polaron. Zbl 1365.35130Frank, Rupert L.; Zhou, Gang 16 2017 Norms of quantum Gaussian multi-mode channels. Zbl 1366.81091Frank, Rupert L.; Lieb, Elliott H. 7 2017 Spectral theory for Schrödinger operators with \(\delta\)-interactions supported on curves in \(\mathbb {R}^3\). Zbl 1378.81026Behrndt, Jussi; Frank, Rupert L.; Kühn, Christian; Lotoreichik, Vladimir; Rohleder, Jonathan 6 2017 Endpoint resolvent estimates for compact Riemannian manifolds. Zbl 1360.58015Frank, Rupert L.; Schimmer, Lukas 5 2017 Spectral cluster bounds for orthonormal systems and oscillatory integral operators in Schatten spaces. Zbl 1373.58015Frank, Rupert L.; Sabin, Julien 3 2017 Eigenvalues of Schrödinger operators with complex surface potentials. Zbl 1372.81057Frank, Rupert L. 2 2017 Averaging of nonlinear Schrödinger equations with strong magnetic confinement. Zbl 1387.35549Frank, Rupert L.; Méhats, Florian; Sparber, Christof 2 2017 Uniqueness of radial solutions for the fractional Laplacian. Zbl 1365.35206Frank, Rupert L.; Lenzmann, Enno; Silvestre, Luis 178 2016 Refined semiclassical asymptotics for fractional powers of the Laplace operator. Zbl 1337.35163Frank, Rupert L.; Geisinger, Leander 27 2016 On the number of eigenvalues of Schrödinger operators with complex potentials. Zbl 1358.35074Frank, Rupert L.; Laptev, Ari; Safronov, Oleg 24 2016 Nonexistence of large nuclei in the liquid drop model. Zbl 1347.49069Frank, Rupert L.; Killip, Rowan; Phan Thành Nam 15 2016 Maximizers for the Stein-Tomas inequality. Zbl 1357.42023Frank, Rupert L.; Lieb, Elliott H.; Sabin, Julien 13 2016 Some operator and trace function convexity theorems. Zbl 1342.47024Carlen, Eric A.; Frank, Rupert L.; Lieb, Elliott H. 11 2016 The external field dependence of the BCS critical temperature. Zbl 1334.82080Frank, Rupert L.; Hainzl, Christian; Seiringer, Robert; Solovej, Jan Philip 8 2016 Multi-component Ginzburg-Landau theory: microscopic derivation and examples. Zbl 1351.82117Frank, Rupert L.; Lemm, Marius 6 2016 The Stein-Tomas inequality in trace ideals. Zbl 1358.35010Frank, Rupert L.; Sabin, Julien 3 2016 Incompatibility of time-dependent Bogoliubov-de-Gennes and Ginzburg-Landau equations. Zbl 1358.82041Frank, Rupert L.; Hainzl, Christian; Schlein, Benjamin; Seiringer, Robert 2 2016 A compactness lemma and its application to the existence of minimizers for the liquid drop model. Zbl 1332.49042Frank, Rupert L.; Lieb, Elliott H. 31 2015 An extension problem for the CR fractional Laplacian. Zbl 1304.35747Frank, Rupert L.; del Mar González, María; Monticelli, Dario D.; Tan, Jinggang 27 2015 Trace class conditions for functions of Schrödinger operators. Zbl 1310.47016Frank, Rupert L.; Pushnitski, Alexander 6 2015 The spectral density of a product of spectral projections. Zbl 1312.81071Frank, Rupert L.; Pushnitski, Alexander 6 2015 The ground state energy of a polaron in a strong magnetic field. Zbl 1323.82045Frank, Rupert L.; Geisinger, Leander 4 2015 Weak perturbations of the \(p\)-Laplacian. Zbl 1322.49076Ekholm, Tomas; Frank, Rupert L.; Kovařík, Hynek 3 2015 Intrinsic metrics for non-local symmetric Dirichlet forms and applications to spectral theory. Zbl 1304.60081Frank, Rupert L.; Lenz, Daniel; Wingert, Daniel 47 2014 Maximizers for Gagliardo-Nirenberg inequalities and related non-local problems. Zbl 1320.46026Bellazzini, Jacopo; Frank, Rupert L.; Visciglia, Nicola 36 2014 Strichartz inequality for orthonormal functions. Zbl 1307.35245Frank, Rupert L.; Lewin, Mathieu; Lieb, Elliott H.; Seiringer, Robert 22 2014 Stability estimates for the lowest eigenvalue of a Schrödinger operator. Zbl 1291.35145Carlen, Eric A.; Frank, Rupert L.; Lieb, Elliott H. 20 2014 Cwikel’s theorem and the CLR inequality. Zbl 1295.35347Frank, Rupert L. 13 2014 Dynamics of a strongly coupled polaron. Zbl 1297.35202Frank, Rupert L.; Schlein, Benjamin 13 2014 Ground state properties of multi-polaron systems. Zbl 1304.82075Frank, R. L.; Lieb, E. H.; Seiringer, R.; Thomas, L. E. 4 2014 Existence of ground states for negative ions at the binding threshold. Zbl 1302.81099Bellazzini, Jacopo; Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert 3 2014 Uniqueness of non-linear ground states for fractional Laplacians in \(\mathbb{R}\). Zbl 1307.35315Frank, Rupert L.; Lenzmann, Enno 182 2013 Monotonicity of a relative Rényi entropy. Zbl 1350.94020Frank, Rupert L.; Lieb, Elliott H. 57 2013 Remainder terms in the fractional Sobolev inequality. Zbl 1296.46032Chen, Shibing; Frank, Rupert L.; Weth, Tobias 23 2013 A positive density analogue of the Lieb-Thirring inequality. Zbl 1260.35088Frank, Rupert L.; Lewin, Mathieu; Lieb, Elliott H.; Seiringer, Robert 19 2013 Extended quantum conditional entropy and quantum uncertainty inequalities. Zbl 1280.81022Frank, Rupert L.; Lieb, Elliott H. 7 2013 Derivation of Ginzburg-Landau theory for a one-dimensional system with contact interaction. Zbl 1277.82073Frank, Rupert L.; Hainzl, Christian; Seiringer, Robert; Solovej, Jan Philip 6 2013 Sharp trace asymptotics for a class of \(2D\)-magnetic operators. (Asymptotiques précisées pour la trace d’une classe d’opérateurs de Schrödinger magnétiques en dimension 2.) Zbl 1301.35070Cornean, Horia D.; Fournais, Søren; Frank, Rupert L.; Helffer, Bernard 5 2013 Heat kernels of metric trees and applications. Zbl 1278.47048Frank, Rupert L.; Kovařík, Hynek 3 2013 Symmetry of bipolaron bound states for small Coulomb repulsion. Zbl 1269.82064Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert 2 2013 Sharp constants in several inequalities on the Heisenberg group. Zbl 1252.42023Frank, Rupert L.; Lieb, Elliott H. 70 2012 A new, rearrangement-free proof of the sharp Hardy-Littlewood-Sobolev inequality. Zbl 1297.39023Frank, Rupert L.; Lieb, Elliott H. 36 2012 Microscopic derivation of Ginzburg-Landau theory. Zbl 1251.35156Frank, Rupert L.; Hainzl, Christian; Seiringer, Robert; Solovej, Jan Philip 28 2012 Hardy-Sobolev-Maz’ya inequalities for arbitrary domains. Zbl 1233.49023Frank, Rupert L.; Loss, Michael 17 2012 Fractional Hardy-Sobolev-Maz’ya inequality for domains. Zbl 1273.26025Dyda, Bartłomiej; Frank, Rupert L. 17 2012 Lieb-Thirring inequality for a model of particles with point interactions. Zbl 1278.81061Frank, Rupert L.; Seiringer, Robert 13 2012 Binding of polarons and atoms at threshold. Zbl 1250.82046Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert 9 2012 Semi-classical analysis of the Laplace operator with Robin boundary conditions. Zbl 1253.35090Frank, Rupert L.; Geisinger, Leander 8 2012 Entropy and the uncertainty principle. Zbl 1256.81022Frank, Rupert L.; Lieb, Elliott H. 4 2012 Eigenvalue bounds for Schrödinger operators with complex potentials. Zbl 1228.35158Frank, Rupert L. 54 2011 A sharp bound on eigenvalues of Schrödinger operators on the half-line with complex-valued potentials. Zbl 1253.35086Frank, Rupert L.; Laptev, Ari; Seiringer, Robert 15 2011 Stability and absence of binding for multi-polaron systems. Zbl 1227.82083Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert; Thomas, Lawrence E. 13 2011 Eigenvalue estimates for Schrödinger operators on metric trees. Zbl 1237.35157Ekholm, Tomas; Frank, Rupert L.; Kovařík, Hynek 9 2011 Critical Lieb-Thirring bounds in gaps and the generalized Nevai conjecture for finite gap Jacobi matrices. Zbl 1229.35157Frank, Rupert L.; Simon, Barry 9 2011 Two-term spectral asymptotics for the Dirichlet Laplacian on a bounded domain. Zbl 1253.47031Frank, Rupert L.; Geisinger, Leander 8 2011 Spherical reflection positivity and the Hardy-Littlewood-Sobolev inequality. Zbl 1378.39013Frank, Rupert L.; Lieb, Elliott H. 5 2011 Weakly coupled bound states of Pauli operators. Zbl 1205.35177Frank, Rupert L.; Morozov, Sergey; Vugalter, Semjon 5 2011 Binding, stability, and non-binding of multi-polaron systems. Zbl 1245.82073Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert; Thomas, Lawrence E. 2 2011 Eigenvalue bounds for Schrödinger operators with a homogeneous magnetic field. Zbl 1231.35129Frank, Rupert L.; Olofsson, Rikard 2 2011 Inversion positivity and the sharp Hardy-Littlewood-Sobolev inequality. Zbl 1204.39024Frank, Rupert L.; Lieb, Elliott H. 51 2010 Sharp fractional Hardy inequalities in half-spaces. Zbl 1185.26044Frank, Rupert L.; Seiringer, Robert 21 2010 Equivalence of Sobolev inequalities and Lieb-Thirring inequalities. Zbl 1203.81072Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert 10 2010 Inequalities between Dirichlet and Neumann eigenvalues on the Heisenberg group. Zbl 1198.35161Frank, Rupert L.; Laptev, Ari 4 2010 A simple proof of Hardy-Lieb-Thirring inequalities. Zbl 1184.35121Frank, Rupert L. 25 2009 Singular spectrum for radial trees. Zbl 1177.05069Breuer, Jonathan; Frank, Rupert L. 16 2009 Pólya’s conjecture in the presence of a constant magnetic field. Zbl 1179.35205Frank, Rupert L.; Loss, Michael; Weidl, Timo 13 2009 ...and 26 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 1,330 Authors 79 Frank, Rupert L. 31 Seiringer, Robert 20 Lieb, Elliott H. 16 Hainzl, Christian 16 Wei, Juncheng 14 Laptev, Ari 14 Lu, Guozhen 14 Phan Thành Nam 13 Cuenin, Jean-Claude 13 Lewin, Mathieu 13 Squassina, Marco 12 Abdellaoui, Boumediene 12 Ambrosio, Vincenzo 12 Solovej, Jan Philip 11 Keller, Matthias 11 Kovařík, Hynek 11 Nguyễn Văn Hoàng 11 Peral Alonso, Ireneo 11 Simon, Barry 10 Hong, Younghun 9 Fournais, Søren 9 González, María del Mar 9 Kachmar, Ayman 9 Lam, Nguyen 9 Liu, Weiming 9 Niu, Miaomiao 9 Sire, Yannick 9 Suragan, Durvudkhan 8 Berta, Mario 8 Christiansen, Jacob Stordal 8 Esfahani, Amin 8 Exner, Pavel 8 Lenz, Daniel H. 8 Lotoreichik, Vladimir 8 Lundholm, Douglas 8 Sabin, Julien 8 Siedentop, Heinz Karl Heinrich 8 Stefanov, Atanas G. 8 Tang, Zhongwei 8 Tomamichel, Marco 8 Topaloglu, Ihsan 7 Ao, Weiwei 7 Chen, Lu 7 Choi, Woocheol 7 Correggi, Michele 7 Hansmann, Marcel 7 Larson, Simon 7 Laugesen, Richard Snyder 7 Lenzmann, Enno 7 Miyagaki, Olimpio Hiroshi 7 Ozawa, Tohru 7 Rougerie, Nicolas 7 Valdinoci, Enrico 7 Yang, Jing 7 Zinchenko, Maxim 6 Alves, Claudianor Oliveira 6 Bellazzini, Jacopo 6 Bez, Neal 6 Borrelli, William 6 Dinh, Van Duong 6 Dipierro, Serena 6 Filippas, Stathis 6 Georgiev, Vladimir S. 6 Hua, Bobo 6 Huang, Xueping 6 König, Tobias 6 Long, Wei 6 Musina, Roberta 6 Niu, Pengcheng 6 Novaga, Matteo 6 Oliveira e Silva, Diogo 6 Peng, Shuangjie 6 Primo, Ana R. M. 6 Rohleder, Jonathan 6 Ruzhansky, Michael V. 6 Tao, Chunxia 6 Tertikas, Achilles 6 Wilde, Mark M. 6 Yang, Jianfu 5 Alama, Stan 5 Barrios Barrera, Begoña 5 Behrndt, Jussi 5 Bhakta, Mousomi 5 Brasco, Lorenzo 5 Bronsard, Lia 5 Carlen, Eric Anders 5 Carrillo de la Plata, José Antonio 5 Chen, Guoyuan 5 Cinti, Eleonora 5 Dolbeault, Jean 5 Ekholm, Tomas 5 Fall, Mouhamed Moustapha 5 Garofalo, Nicola 5 Gesztesy, Fritz 5 Gontier, David 5 Grubb, Gerd 5 Hajaiej, Hichem 5 Kassymov, Aidyn Adilovich 5 Kim, Seunghyeok 5 Knüpfer, Hans ...and 1,230 more Authors all top 5 Cited in 228 Serials 81 Journal of Mathematical Physics 66 Calculus of Variations and Partial Differential Equations 60 Journal of Functional Analysis 58 Communications in Mathematical Physics 48 Nonlinear Analysis. Theory, Methods & Applications. 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Second Series 2 Pacific Journal of Mathematics ...and 128 more Serials all top 5 Cited in 52 Fields 879 Partial differential equations (35-XX) 302 Quantum theory (81-XX) 240 Operator theory (47-XX) 160 Functional analysis (46-XX) 140 Real functions (26-XX) 108 Statistical mechanics, structure of matter (82-XX) 105 Calculus of variations and optimal control; optimization (49-XX) 68 Global analysis, analysis on manifolds (58-XX) 66 Harmonic analysis on Euclidean spaces (42-XX) 54 Information and communication theory, circuits (94-XX) 51 Integral equations (45-XX) 51 Probability theory and stochastic processes (60-XX) 48 Differential geometry (53-XX) 40 Ordinary differential equations (34-XX) 36 Potential theory (31-XX) 29 Combinatorics (05-XX) 25 Difference and functional equations (39-XX) 18 Fluid mechanics (76-XX) 17 Linear and multilinear algebra; matrix theory (15-XX) 17 Numerical analysis (65-XX) 15 Optics, electromagnetic theory (78-XX) 14 Abstract harmonic analysis (43-XX) 13 Topological groups, Lie groups (22-XX) 13 Several complex variables and analytic spaces (32-XX) 12 Measure and integration (28-XX) 12 Dynamical systems and ergodic theory (37-XX) 11 Special functions (33-XX) 10 Relativity and gravitational theory (83-XX) 9 Functions of a complex variable (30-XX) 9 Convex and discrete geometry (52-XX) 8 Mechanics of deformable solids (74-XX) 8 Astronomy and astrophysics (85-XX) 7 Mechanics of particles and systems (70-XX) 6 Manifolds and cell complexes (57-XX) 5 Integral transforms, operational calculus (44-XX) 5 Statistics (62-XX) 4 Number theory (11-XX) 3 Algebraic geometry (14-XX) 3 Group theory and generalizations (20-XX) 3 Geometry (51-XX) 3 Classical thermodynamics, heat transfer (80-XX) 2 General and overarching topics; collections (00-XX) 2 History and biography (01-XX) 2 Nonassociative rings and algebras (17-XX) 2 Approximations and expansions (41-XX) 2 Computer science (68-XX) 2 Operations research, mathematical programming (90-XX) 2 Biology and other natural sciences (92-XX) 1 Commutative algebra (13-XX) 1 Sequences, series, summability (40-XX) 1 Algebraic topology (55-XX) 1 Geophysics (86-XX) Citations by Year