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Frank, Rupert L.

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Author ID: frank.rupert-l Recent zbMATH articles by "Frank, Rupert L."
Published as: Frank, Rupert L.; Frank, R. L.; Frank, Rupert
External Links: MGP
Documents Indexed: 133 Publications since 2003, including 1 Book
all top 5

Co-Authors

13 single-authored
31 Lieb, Elliott H.
24 Seiringer, Robert
8 Hainzl, Christian
7 Laptev, Ari
5 Carlen, Eric Anders
5 Ekholm, Tomas
5 König, Tobias
5 Kovařík, Hynek
5 Phan Thành Nam
5 Sabin, Julien
5 Simon, Barry
4 Geisinger, Leander
4 Pushnitski, Alexander B.
4 Siedentop, Heinz Karl Heinrich
4 Solovej, Jan Philip
3 Lewin, Mathieu
3 Loss, Michael
3 Thomas, Lawrence E.
3 Van Den Bosch, Hanne
3 Weidl, Timo
2 Bellazzini, Jacopo
2 Benguria, Rafael D.
2 Exner, Pavel
2 Ivanisvili, Paata
2 Larson, Simon
2 Lemm, Marius
2 Lenzmann, Enno
2 Merz, Konstantin
2 Safronov, Oleg
2 Schlein, Benjamin
2 Shterenberg, Roman G.
2 Warzel, Simone
1 Behrndt, Jussi
1 Borrelli, William
1 Breuer, Jonathan
1 Carrillo de la Plata, José Antonio
1 Chen, Shibing
1 Cornean, Horia D.
1 Delgadino, Matias Gonzalo
1 Dolbeault, Jean
1 Dyda, Bartłomiej
1 Emmert, Lukas
1 Fournais, Søren
1 Gang, Zhou
1 Gesztesy, Fritz
1 Gontier, David
1 González, María del Mar
1 Hansson, Anders M.
1 Helffer, Bernard
1 Hoffmann, Franca
1 Holden, Helge
1 Hundertmark, Dirk
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 Schimmer, Lukas
1 Sparber, Christof
1 Tan, Jinggang
1 Tang, Hanli
1 Visciglia, Nicola
1 Vugalter, Semjon A.
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 Annales Henri Poincaré
6 Journal of Mathematical Physics
6 Journal of Functional Analysis
6 Calculus of Variations and Partial Differential Equations
5 Advances in Mathematics
4 Journal of the European Mathematical Society (JEMS)
3 Communications on Pure and Applied Mathematics
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 Journal für die Reine und Angewandte Mathematik
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 Publications Mathématiques
1 Journal of the London Mathematical Society. Second Series
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 Linear Algebra and its Applications
1 St. Petersburg Mathematical Journal
1 Mathematical Research Letters
1 Annals of Mathematics. Second Series
1 Communications in Mathematical Sciences
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

Publications by Year

Citations contained in zbMATH Open

113 Publications have been cited 1,755 times in 1,130 Documents Cited by Year
Uniqueness of non-linear ground states for fractional Laplacians in \(\mathbb{R}\). Zbl 1307.35315
Frank, Rupert L.; Lenzmann, Enno
150
2013
Uniqueness of radial solutions for the fractional Laplacian. Zbl 1365.35206
Frank, Rupert L.; Lenzmann, Enno; Silvestre, Luis
147
2016
Nonlinear ground state representations and sharp Hardy inequalities. Zbl 1189.26031
Frank, Rupert L.; Seiringer, Robert
128
2008
Hardy-Lieb-Thirring inequalities for fractional Schrödinger operators. Zbl 1202.35146
Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert
117
2008
Sharp constants in several inequalities on the Heisenberg group. Zbl 1252.42023
Frank, Rupert L.; Lieb, Elliott H.
62
2012
Monotonicity of a relative Rényi entropy. Zbl 1350.94020
Frank, Rupert L.; Lieb, Elliott H.
49
2013
Inversion positivity and the sharp Hardy-Littlewood-Sobolev inequality. Zbl 1204.39024
Frank, Rupert L.; Lieb, Elliott H.
46
2010
Eigenvalue bounds for Schrödinger operators with complex potentials. Zbl 1228.35158
Frank, Rupert L.
44
2011
Intrinsic metrics for non-local symmetric Dirichlet forms and applications to spectral theory. Zbl 1304.60081
Frank, Rupert L.; Lenz, Daniel; Wingert, Daniel
44
2014
Lieb-Thirring inequalities for Schrödinger operators with complex-valued potentials. Zbl 1160.81382
Frank, Rupert L.; Laptev, Ari; Lieb, Elliott H.; Seiringer, Robert
40
2006
Maximizers for Gagliardo-Nirenberg inequalities and related non-local problems. Zbl 1320.46026
Bellazzini, Jacopo; Frank, Rupert L.; Visciglia, Nicola
34
2014
The sharp constant in the Hardy-Sobolev-Maz’ya inequality in the three-dimensional upper half space. Zbl 1173.26011
Benguria, Rafael D.; Frank, Rupert L.; Loss, Michael
31
2008
Restriction theorems for orthonormal functions, Strichartz inequalities, and uniform Sobolev estimates. Zbl 1388.42018
Frank, Rupert L.; Sabin, Julien
31
2017
A new, rearrangement-free proof of the sharp Hardy-Littlewood-Sobolev inequality. Zbl 1297.39023
Frank, Rupert L.; Lieb, Elliott H.
28
2012
The critical temperature for the BCS equation at weak coupling. Zbl 1137.82025
Frank, Rupert L.; Hainzl, Christian; Naboko, Serguei; Seiringer, Robert
27
2007
Microscopic derivation of Ginzburg-Landau theory. Zbl 1251.35156
Frank, Rupert L.; Hainzl, Christian; Seiringer, Robert; Solovej, Jan Philip
27
2012
Eigenvalue bounds for Schrödinger operators with complex potentials. III. Zbl 1390.35204
Frank, Rupert L.
24
2018
A compactness lemma and its application to the existence of minimizers for the liquid drop model. Zbl 1332.49042
Frank, Rupert L.; Lieb, Elliott H.
24
2015
On Lieb-Thirring inequalities for Schrödinger operators with virtual level. Zbl 1106.81039
Ekholm, T.; Frank, R. L.
23
2006
A simple proof of Hardy-Lieb-Thirring inequalities. Zbl 1184.35121
Frank, Rupert L.
22
2009
Refined semiclassical asymptotics for fractional powers of the Laplace operator. Zbl 1337.35163
Frank, Rupert L.; Geisinger, Leander
22
2016
Eigenvalue bounds for Schrödinger operators with complex potentials II. Zbl 1386.35061
Frank, Rupert L.; Simon, Barry
21
2017
Remainder terms in the fractional Sobolev inequality. Zbl 1296.46032
Chen, Shibing; Frank, Rupert L.; Weth, Tobias
20
2013
Sharp fractional Hardy inequalities in half-spaces. Zbl 1185.26044
Frank, Rupert L.; Seiringer, Robert
20
2010
Strichartz inequality for orthonormal functions. Zbl 1307.35245
Frank, Rupert L.; Lewin, Mathieu; Lieb, Elliott H.; Seiringer, Robert
20
2014
An extension problem for the CR fractional Laplacian. Zbl 1304.35747
Frank, Rupert L.; del Mar González, María; Monticelli, Dario D.; Tan, Jinggang
20
2015
On the number of eigenvalues of Schrödinger operators with complex potentials. Zbl 1358.35074
Frank, Rupert L.; Laptev, Ari; Safronov, Oleg
20
2016
A positive density analogue of the Lieb-Thirring inequality. Zbl 1260.35088
Frank, Rupert L.; Lewin, Mathieu; Lieb, Elliott H.; Seiringer, Robert
19
2013
Stability estimates for the lowest eigenvalue of a Schrödinger operator. Zbl 1291.35145
Carlen, Eric A.; Frank, Rupert L.; Lieb, Elliott H.
18
2014
Fractional Hardy-Sobolev-Maz’ya inequality for domains. Zbl 1273.26025
Dyda, Bartłomiej; Frank, Rupert L.
14
2012
Eigenvalue bounds for perturbations of Schrödinger operators and Jacobi matrices with regular ground states. Zbl 1158.35021
Frank, Rupert L.; Simon, Barry; Weidl, Timo
13
2008
Stability and absence of binding for multi-polaron systems. Zbl 1227.82083
Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert; Thomas, Lawrence E.
13
2011
Hardy-Sobolev-Maz’ya inequalities for arbitrary domains. Zbl 1233.49023
Frank, Rupert L.; Loss, Michael
13
2012
Pólya’s conjecture in the presence of a constant magnetic field. Zbl 1179.35205
Frank, Rupert L.; Loss, Michael; Weidl, Timo
13
2009
Singular spectrum for radial trees. Zbl 1177.05069
Breuer, Jonathan; Frank, Rupert L.
13
2009
Derivation of an effective evolution equation for a strongly coupled polaron. Zbl 1365.35130
Frank, Rupert L.; Zhou, Gang
13
2017
A sharp bound on eigenvalues of Schrödinger operators on the half-line with complex-valued potentials. Zbl 1253.35086
Frank, Rupert L.; Laptev, Ari; Seiringer, Robert
12
2011
Classification of positive singular solutions to a nonlinear biharmonic equation with critical exponent. Zbl 1421.35150
Frank, Rupert L.; König, Tobias
12
2019
Lieb-Thirring inequality for a model of particles with point interactions. Zbl 1278.81061
Frank, Rupert L.; Seiringer, Robert
12
2012
Cwikel’s theorem and the CLR inequality. Zbl 1295.35347
Frank, Rupert L.
11
2014
The ionization conjecture in Thomas-Fermi-Dirac-von Weizsäcker theory. Zbl 1386.49063
Frank, Rupert L.; Phan Thành Nam; Van Den Bosch, Hanne
11
2018
Nonexistence of large nuclei in the liquid drop model. Zbl 1347.49069
Frank, Rupert L.; Killip, Rowan; Phan Thành Nam
11
2016
Dynamics of a strongly coupled polaron. Zbl 1297.35202
Frank, Rupert L.; Schlein, Benjamin
11
2014
Maximizers for the Stein-Tomas inequality. Zbl 1357.42023
Frank, Rupert L.; Lieb, Elliott H.; Sabin, Julien
11
2016
Stability of relativistic matter with magnetic fields for nuclear charges up to the critical value. Zbl 1135.81030
Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert
10
2007
Equivalence of Sobolev inequalities and Lieb-Thirring inequalities. Zbl 1203.81072
Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert
10
2010
Some operator and trace function convexity theorems. Zbl 1342.47024
Carlen, Eric A.; Frank, Rupert L.; Lieb, Elliott H.
10
2016
Critical Lieb-Thirring bounds in gaps and the generalized Nevai conjecture for finite gap Jacobi matrices. Zbl 1229.35157
Frank, Rupert L.; Simon, Barry
9
2011
Binding of polarons and atoms at threshold. Zbl 1250.82046
Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert
9
2012
The ground state energy of heavy atoms: Relativistic lowering of the leading energy correction. Zbl 1162.81037
Frank, Rupert L.; Siedentop, Heinz; Warzel, Simone
9
2008
On the asymptotic number of edge states for magnetic Schrödinger operators. Zbl 1131.35076
Frank, Rupert L.
9
2007
Inequalities for quantum divergences and the Audenaert-Datta conjecture. Zbl 1414.81064
Carlen, Eric A.; Frank, Rupert L.; Lieb, Elliott H.
8
2018
The external field dependence of the BCS critical temperature. Zbl 1334.82080
Frank, Rupert L.; Hainzl, Christian; Seiringer, Robert; Solovej, Jan Philip
8
2016
Eigenvalue estimates for Schrödinger operators on metric trees. Zbl 1237.35157
Ekholm, Tomas; Frank, Rupert L.; Kovařík, Hynek
7
2011
The energy of heavy atoms according to Brown and Ravenhall: the Scott correction. Zbl 1186.81137
Frank, Rupert L.; Siedentop, Heinz; Warzel, Simone
7
2009
Minimizers for the fractional Sobolev inequality on domains. Zbl 1393.26026
Frank, Rupert L.; Jin, Tianling; Xiong, Jingang
7
2018
A “liquid-solid” phase transition in a simple model for swarming, based on the “no flat-spots” theorem for subharmonic functions. Zbl 1420.49040
Frank, Rupert; Lieb, Elliott H.
7
2018
Norms of quantum Gaussian multi-mode channels. Zbl 1366.81091
Frank, Rupert L.; Lieb, Elliott H.
7
2017
Spectral inequalities for Schrödinger operators with surface potentials. Zbl 1170.35486
Frank, Rupert L.; Laptev, Ari
6
2008
Trace class conditions for functions of Schrödinger operators. Zbl 1310.47016
Frank, Rupert L.; Pushnitski, Alexander
6
2015
Two-term spectral asymptotics for the Dirichlet Laplacian on a bounded domain. Zbl 1253.47031
Frank, Rupert L.; Geisinger, Leander
6
2011
Semi-classical analysis of the Laplace operator with Robin boundary conditions. Zbl 1253.35090
Frank, Rupert L.; Geisinger, Leander
6
2012
The spectral density of a product of spectral projections. Zbl 1312.81071
Frank, Rupert L.; Pushnitski, Alexander
6
2015
Derivation of Ginzburg-Landau theory for a one-dimensional system with contact interaction. Zbl 1277.82073
Frank, Rupert L.; Hainzl, Christian; Seiringer, Robert; Solovej, Jan Philip
6
2013
Extended quantum conditional entropy and quantum uncertainty inequalities. Zbl 1280.81022
Frank, Rupert L.; Lieb, Elliott H.
6
2013
Spectral theory for Schrödinger operators with \(\delta\)-interactions supported on curves in \(\mathbb {R}^3\). Zbl 1378.81026
Behrndt, Jussi; Frank, Rupert L.; Kühn, Christian; Lotoreichik, Vladimir; Rohleder, Jonathan
6
2017
Eigenvalue estimates for magnetic Schrödinger operators in domains. Zbl 1186.35119
Frank, Rupert L.; Laptev, Ari; Molchanov, Stanislav
5
2008
Lieb-Thirring inequalities on the half-line with critical exponent. Zbl 1147.35020
Ekholm, Tomas; Frank, Rupert L.
5
2008
Absolute continuity of the spectrum for periodically modulated leaky wires in \({\mathbb{R}^{3}}\). Zbl 1206.82112
Exner, Pavel; Frank, Rupert L.
5
2007
Sharp decay estimates for critical Dirac equations. Zbl 1435.35053
Borrelli, William; Frank, Rupert L.
5
2020
Multi-component Ginzburg-Landau theory: microscopic derivation and examples. Zbl 1351.82117
Frank, Rupert L.; Lemm, Marius
5
2016
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 1301.35070
Cornean, Horia D.; Fournais, Søren; Frank, Rupert L.; Helffer, Bernard
5
2013
On the scattering theory of the Laplacian with a periodic boundary condition. I. Existence of wave operators. Zbl 1142.35374
Frank, Rupert L.
4
2003
Spherical reflection positivity and the Hardy-Littlewood-Sobolev inequality. Zbl 1378.39013
Frank, Rupert L.; Lieb, Elliott H.
4
2011
Weakly coupled bound states of Pauli operators. Zbl 1205.35177
Frank, Rupert L.; Morozov, Sergey; Vugalter, Semjon
4
2011
The ground state energy of a polaron in a strong magnetic field. Zbl 1323.82045
Frank, Rupert L.; Geisinger, Leander
4
2015
Entropy and the uncertainty principle. Zbl 1256.81022
Frank, Rupert L.; Lieb, Elliott H.
4
2012
Number of bound states of Schrödinger operators with matrix-valued potentials. Zbl 1135.35052
Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert
4
2007
Remarks on eigenvalue estimates and semigroup domination. Zbl 1183.81068
Frank, Rupert L.
4
2009
Endpoint resolvent estimates for compact Riemannian manifolds. Zbl 1360.58015
Frank, Rupert L.; Schimmer, Lukas
4
2017
Eigenvalue bounds for the fractional Laplacian: a review. Zbl 1404.35303
Frank, Rupert L.
3
2018
On the scattering theory of the Laplacian with a periodic boundary condition. II. Additional channels of scattering. Zbl 1210.35040
Frank, Rupert L.; Shterenberg, Roman G.
3
2004
Remarks about Hardy inequalities on metric trees. Zbl 1175.26035
Ekholm, Tomas; Frank, Rupert L.; Kovařík, Hynek
3
2008
On the tunneling effect for magnetic Schrödinger operators in antidot lattices. Zbl 1157.81309
Frank, Rupert L.
3
2006
Existence of ground states for negative ions at the binding threshold. Zbl 1302.81099
Bellazzini, Jacopo; Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert
3
2014
Weak perturbations of the \(p\)-Laplacian. Zbl 1322.49076
Ekholm, Tomas; Frank, Rupert L.; Kovařík, Hynek
3
2015
Inequalities between Dirichlet and Neumann eigenvalues on the Heisenberg group. Zbl 1198.35161
Frank, Rupert L.; Laptev, Ari
3
2010
Heat kernels of metric trees and applications. Zbl 1278.47048
Frank, Rupert L.; Kovařík, Hynek
3
2013
A non-linear adiabatic theorem for the one-dimensional Landau-Pekar equations. Zbl 1445.35128
Frank, Rupert L.; Gang, Zhou
3
2020
Kato smoothness and functions of perturbed self-adjoint operators. Zbl 07078811
Frank, Rupert L.; Pushnitski, Alexander
3
2019
The maximal excess charge in Müller density-matrix-functional theory. Zbl 1397.81456
Frank, Rupert L.; Phan Thành Nam; van den Bosch, Hanne
3
2018
The Stein-Tomas inequality in trace ideals. Zbl 1358.35010
Frank, Rupert L.; Sabin, Julien
3
2016
Eigenvalue estimates for the Aharonov-Bohm operator in a domain. Zbl 1171.35090
Frank, Rupert L.; Hansson, Anders M.
2
2009
Binding, stability, and non-binding of multi-polaron systems. Zbl 1245.82073
Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert; Thomas, Lawrence E.
2
2011
Eigenvalue bounds for Schrödinger operators with a homogeneous magnetic field. Zbl 1231.35129
Frank, Rupert L.; Olofsson, Rikard
2
2011
Absolutely continuous spectrum of a class of random nonergodic Schrödinger operators. Zbl 1087.60052
Frank, R. L.; Safronov, O.
2
2005
Schatten class conditions for functions of Schrödinger operators. Zbl 07120692
Frank, Rupert L.; Pushnitski, Alexander
2
2019
On the spectrum of partially periodic operators. Zbl 1210.35041
Frank, Rupert L.; Shterenberg, Roman G.
2
2007
Spectral cluster bounds for orthonormal systems and oscillatory integral operators in Schatten spaces. Zbl 1373.58015
Frank, Rupert L.; Sabin, Julien
2
2017
Eigenvalues of Schrödinger operators with complex surface potentials. Zbl 1372.81057
Frank, Rupert L.
2
2017
Non-degeneracy for the critical Lane-Emden system. Zbl 1464.35097
Frank, Rupert L.; Kim, Seunghyeok; Pistoia, Angela
1
2021
Sharp decay estimates for critical Dirac equations. Zbl 1435.35053
Borrelli, William; Frank, Rupert L.
5
2020
A non-linear adiabatic theorem for the one-dimensional Landau-Pekar equations. Zbl 1445.35128
Frank, Rupert L.; Gang, Zhou
3
2020
Inequalities that sharpen the triangle inequality for sums of \(N\) functions in \(L^p\). Zbl 07201278
Carlen, Eric A.; Frank, Rupert L.; Lieb, Elliott H.
1
2020
Classification of positive singular solutions to a nonlinear biharmonic equation with critical exponent. Zbl 1421.35150
Frank, Rupert L.; König, Tobias
12
2019
Kato smoothness and functions of perturbed self-adjoint operators. Zbl 07078811
Frank, Rupert L.; Pushnitski, Alexander
3
2019
Schatten class conditions for functions of Schrödinger operators. Zbl 07120692
Frank, Rupert L.; Pushnitski, Alexander
2
2019
Periodic energy minimizers for a one-dimensional liquid drop model. Zbl 1428.82062
Frank, Rupert L.; Lieb, Elliott H.
1
2019
Reverse Hardy-Littlewood-Sobolev inequalities. Zbl 1442.35011
Carrillo, José A.; Delgadino, Matías G.; Dolbeault, Jean; Frank, Rupert L.; Hoffmann, Franca
1
2019
Singular solutions to a semilinear biharmonic equation with a general critical nonlinearity. Zbl 1454.35102
Frank, Rupert L.; König, Tobias
1
2019
Eigenvalue bounds for Schrödinger operators with complex potentials. III. Zbl 1390.35204
Frank, Rupert L.
24
2018
The ionization conjecture in Thomas-Fermi-Dirac-von Weizsäcker theory. Zbl 1386.49063
Frank, Rupert L.; Phan Thành Nam; Van Den Bosch, Hanne
11
2018
Inequalities for quantum divergences and the Audenaert-Datta conjecture. Zbl 1414.81064
Carlen, Eric A.; Frank, Rupert L.; Lieb, Elliott H.
8
2018
Minimizers for the fractional Sobolev inequality on domains. Zbl 1393.26026
Frank, Rupert L.; Jin, Tianling; Xiong, Jingang
7
2018
A “liquid-solid” phase transition in a simple model for swarming, based on the “no flat-spots” theorem for subharmonic functions. Zbl 1420.49040
Frank, Rupert; Lieb, Elliott H.
7
2018
Eigenvalue bounds for the fractional Laplacian: a review. Zbl 1404.35303
Frank, Rupert L.
3
2018
The maximal excess charge in Müller density-matrix-functional theory. Zbl 1397.81456
Frank, Rupert L.; Phan Thành Nam; van den Bosch, Hanne
3
2018
A short proof of the ionization conjecture in Müller theory. Zbl 1423.81198
Frank, Rupert L.; Phan Thành Nam; Van Den Bosch, Hanne
1
2018
Extremizers for the Airy-Strichartz inequality. Zbl 1406.35354
Frank, Rupert L.; Sabin, Julien
1
2018
Restriction theorems for orthonormal functions, Strichartz inequalities, and uniform Sobolev estimates. Zbl 1388.42018
Frank, Rupert L.; Sabin, Julien
31
2017
Eigenvalue bounds for Schrödinger operators with complex potentials II. Zbl 1386.35061
Frank, Rupert L.; Simon, Barry
21
2017
Derivation of an effective evolution equation for a strongly coupled polaron. Zbl 1365.35130
Frank, Rupert L.; Zhou, Gang
13
2017
Norms of quantum Gaussian multi-mode channels. Zbl 1366.81091
Frank, Rupert L.; Lieb, Elliott H.
7
2017
Spectral theory for Schrödinger operators with \(\delta\)-interactions supported on curves in \(\mathbb {R}^3\). Zbl 1378.81026
Behrndt, Jussi; Frank, Rupert L.; Kühn, Christian; Lotoreichik, Vladimir; Rohleder, Jonathan
6
2017
Endpoint resolvent estimates for compact Riemannian manifolds. Zbl 1360.58015
Frank, Rupert L.; Schimmer, Lukas
4
2017
Spectral cluster bounds for orthonormal systems and oscillatory integral operators in Schatten spaces. Zbl 1373.58015
Frank, Rupert L.; Sabin, Julien
2
2017
Eigenvalues of Schrödinger operators with complex surface potentials. Zbl 1372.81057
Frank, Rupert L.
2
2017
Averaging of nonlinear Schrödinger equations with strong magnetic confinement. Zbl 1387.35549
Frank, Rupert L.; Méhats, Florian; Sparber, Christof
1
2017
Uniqueness of radial solutions for the fractional Laplacian. Zbl 1365.35206
Frank, Rupert L.; Lenzmann, Enno; Silvestre, Luis
147
2016
Refined semiclassical asymptotics for fractional powers of the Laplace operator. Zbl 1337.35163
Frank, Rupert L.; Geisinger, Leander
22
2016
On the number of eigenvalues of Schrödinger operators with complex potentials. Zbl 1358.35074
Frank, Rupert L.; Laptev, Ari; Safronov, Oleg
20
2016
Nonexistence of large nuclei in the liquid drop model. Zbl 1347.49069
Frank, Rupert L.; Killip, Rowan; Phan Thành Nam
11
2016
Maximizers for the Stein-Tomas inequality. Zbl 1357.42023
Frank, Rupert L.; Lieb, Elliott H.; Sabin, Julien
11
2016
Some operator and trace function convexity theorems. Zbl 1342.47024
Carlen, Eric A.; Frank, Rupert L.; Lieb, Elliott H.
10
2016
The external field dependence of the BCS critical temperature. Zbl 1334.82080
Frank, Rupert L.; Hainzl, Christian; Seiringer, Robert; Solovej, Jan Philip
8
2016
Multi-component Ginzburg-Landau theory: microscopic derivation and examples. Zbl 1351.82117
Frank, Rupert L.; Lemm, Marius
5
2016
The Stein-Tomas inequality in trace ideals. Zbl 1358.35010
Frank, Rupert L.; Sabin, Julien
3
2016
Incompatibility of time-dependent Bogoliubov-de-Gennes and Ginzburg-Landau equations. Zbl 1358.82041
Frank, 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 1332.49042
Frank, Rupert L.; Lieb, Elliott H.
24
2015
An extension problem for the CR fractional Laplacian. Zbl 1304.35747
Frank, Rupert L.; del Mar González, María; Monticelli, Dario D.; Tan, Jinggang
20
2015
Trace class conditions for functions of Schrödinger operators. Zbl 1310.47016
Frank, Rupert L.; Pushnitski, Alexander
6
2015
The spectral density of a product of spectral projections. Zbl 1312.81071
Frank, Rupert L.; Pushnitski, Alexander
6
2015
The ground state energy of a polaron in a strong magnetic field. Zbl 1323.82045
Frank, Rupert L.; Geisinger, Leander
4
2015
Weak perturbations of the \(p\)-Laplacian. Zbl 1322.49076
Ekholm, Tomas; Frank, Rupert L.; Kovařík, Hynek
3
2015
Intrinsic metrics for non-local symmetric Dirichlet forms and applications to spectral theory. Zbl 1304.60081
Frank, Rupert L.; Lenz, Daniel; Wingert, Daniel
44
2014
Maximizers for Gagliardo-Nirenberg inequalities and related non-local problems. Zbl 1320.46026
Bellazzini, Jacopo; Frank, Rupert L.; Visciglia, Nicola
34
2014
Strichartz inequality for orthonormal functions. Zbl 1307.35245
Frank, Rupert L.; Lewin, Mathieu; Lieb, Elliott H.; Seiringer, Robert
20
2014
Stability estimates for the lowest eigenvalue of a Schrödinger operator. Zbl 1291.35145
Carlen, Eric A.; Frank, Rupert L.; Lieb, Elliott H.
18
2014
Cwikel’s theorem and the CLR inequality. Zbl 1295.35347
Frank, Rupert L.
11
2014
Dynamics of a strongly coupled polaron. Zbl 1297.35202
Frank, Rupert L.; Schlein, Benjamin
11
2014
Existence of ground states for negative ions at the binding threshold. Zbl 1302.81099
Bellazzini, Jacopo; Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert
3
2014
Ground state properties of multi-polaron systems. Zbl 1304.82075
Frank, R. L.; Lieb, E. H.; Seiringer, R.; Thomas, L. E.
2
2014
Uniqueness of non-linear ground states for fractional Laplacians in \(\mathbb{R}\). Zbl 1307.35315
Frank, Rupert L.; Lenzmann, Enno
150
2013
Monotonicity of a relative Rényi entropy. Zbl 1350.94020
Frank, Rupert L.; Lieb, Elliott H.
49
2013
Remainder terms in the fractional Sobolev inequality. Zbl 1296.46032
Chen, Shibing; Frank, Rupert L.; Weth, Tobias
20
2013
A positive density analogue of the Lieb-Thirring inequality. Zbl 1260.35088
Frank, Rupert L.; Lewin, Mathieu; Lieb, Elliott H.; Seiringer, Robert
19
2013
Derivation of Ginzburg-Landau theory for a one-dimensional system with contact interaction. Zbl 1277.82073
Frank, Rupert L.; Hainzl, Christian; Seiringer, Robert; Solovej, Jan Philip
6
2013
Extended quantum conditional entropy and quantum uncertainty inequalities. Zbl 1280.81022
Frank, Rupert L.; Lieb, Elliott H.
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 1301.35070
Cornean, Horia D.; Fournais, Søren; Frank, Rupert L.; Helffer, Bernard
5
2013
Heat kernels of metric trees and applications. Zbl 1278.47048
Frank, Rupert L.; Kovařík, Hynek
3
2013
Symmetry of bipolaron bound states for small Coulomb repulsion. Zbl 1269.82064
Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert
1
2013
Sharp constants in several inequalities on the Heisenberg group. Zbl 1252.42023
Frank, Rupert L.; Lieb, Elliott H.
62
2012
A new, rearrangement-free proof of the sharp Hardy-Littlewood-Sobolev inequality. Zbl 1297.39023
Frank, Rupert L.; Lieb, Elliott H.
28
2012
Microscopic derivation of Ginzburg-Landau theory. Zbl 1251.35156
Frank, Rupert L.; Hainzl, Christian; Seiringer, Robert; Solovej, Jan Philip
27
2012
Fractional Hardy-Sobolev-Maz’ya inequality for domains. Zbl 1273.26025
Dyda, Bartłomiej; Frank, Rupert L.
14
2012
Hardy-Sobolev-Maz’ya inequalities for arbitrary domains. Zbl 1233.49023
Frank, Rupert L.; Loss, Michael
13
2012
Lieb-Thirring inequality for a model of particles with point interactions. Zbl 1278.81061
Frank, Rupert L.; Seiringer, Robert
12
2012
Binding of polarons and atoms at threshold. Zbl 1250.82046
Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert
9
2012
Semi-classical analysis of the Laplace operator with Robin boundary conditions. Zbl 1253.35090
Frank, Rupert L.; Geisinger, Leander
6
2012
Entropy and the uncertainty principle. Zbl 1256.81022
Frank, Rupert L.; Lieb, Elliott H.
4
2012
Eigenvalue bounds for Schrödinger operators with complex potentials. Zbl 1228.35158
Frank, Rupert L.
44
2011
Stability and absence of binding for multi-polaron systems. Zbl 1227.82083
Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert; Thomas, Lawrence E.
13
2011
A sharp bound on eigenvalues of Schrödinger operators on the half-line with complex-valued potentials. Zbl 1253.35086
Frank, Rupert L.; Laptev, Ari; Seiringer, Robert
12
2011
Critical Lieb-Thirring bounds in gaps and the generalized Nevai conjecture for finite gap Jacobi matrices. Zbl 1229.35157
Frank, Rupert L.; Simon, Barry
9
2011
Eigenvalue estimates for Schrödinger operators on metric trees. Zbl 1237.35157
Ekholm, Tomas; Frank, Rupert L.; Kovařík, Hynek
7
2011
Two-term spectral asymptotics for the Dirichlet Laplacian on a bounded domain. Zbl 1253.47031
Frank, Rupert L.; Geisinger, Leander
6
2011
Spherical reflection positivity and the Hardy-Littlewood-Sobolev inequality. Zbl 1378.39013
Frank, Rupert L.; Lieb, Elliott H.
4
2011
Weakly coupled bound states of Pauli operators. Zbl 1205.35177
Frank, Rupert L.; Morozov, Sergey; Vugalter, Semjon
4
2011
Binding, stability, and non-binding of multi-polaron systems. Zbl 1245.82073
Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert; Thomas, Lawrence E.
2
2011
Eigenvalue bounds for Schrödinger operators with a homogeneous magnetic field. Zbl 1231.35129
Frank, Rupert L.; Olofsson, Rikard
2
2011
Inversion positivity and the sharp Hardy-Littlewood-Sobolev inequality. Zbl 1204.39024
Frank, Rupert L.; Lieb, Elliott H.
46
2010
Sharp fractional Hardy inequalities in half-spaces. Zbl 1185.26044
Frank, Rupert L.; Seiringer, Robert
20
2010
Equivalence of Sobolev inequalities and Lieb-Thirring inequalities. Zbl 1203.81072
Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert
10
2010
Inequalities between Dirichlet and Neumann eigenvalues on the Heisenberg group. Zbl 1198.35161
Frank, Rupert L.; Laptev, Ari
3
2010
A simple proof of Hardy-Lieb-Thirring inequalities. Zbl 1184.35121
Frank, Rupert L.
22
2009
Pólya’s conjecture in the presence of a constant magnetic field. Zbl 1179.35205
Frank, Rupert L.; Loss, Michael; Weidl, Timo
13
2009
Singular spectrum for radial trees. Zbl 1177.05069
Breuer, Jonathan; Frank, Rupert L.
13
2009
The energy of heavy atoms according to Brown and Ravenhall: the Scott correction. Zbl 1186.81137
Frank, Rupert L.; Siedentop, Heinz; Warzel, Simone
7
2009
Remarks on eigenvalue estimates and semigroup domination. Zbl 1183.81068
Frank, Rupert L.
4
2009
Eigenvalue estimates for the Aharonov-Bohm operator in a domain. Zbl 1171.35090
Frank, Rupert L.; Hansson, Anders M.
2
2009
A note on low energy scattering for homogeneous long-range potentials. Zbl 1205.81128
Frank, Rupert L.
1
2009
Nonlinear ground state representations and sharp Hardy inequalities. Zbl 1189.26031
Frank, Rupert L.; Seiringer, Robert
128
2008
Hardy-Lieb-Thirring inequalities for fractional Schrödinger operators. Zbl 1202.35146
Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert
117
2008
The sharp constant in the Hardy-Sobolev-Maz’ya inequality in the three-dimensional upper half space. Zbl 1173.26011
Benguria, Rafael D.; Frank, Rupert L.; Loss, Michael
31
2008
Eigenvalue bounds for perturbations of Schrödinger operators and Jacobi matrices with regular ground states. Zbl 1158.35021
Frank, Rupert L.; Simon, Barry; Weidl, Timo
13
2008
The ground state energy of heavy atoms: Relativistic lowering of the leading energy correction. Zbl 1162.81037
Frank, Rupert L.; Siedentop, Heinz; Warzel, Simone
9
2008
Spectral inequalities for Schrödinger operators with surface potentials. Zbl 1170.35486
Frank, Rupert L.; Laptev, Ari
6
2008
Eigenvalue estimates for magnetic Schrödinger operators in domains. Zbl 1186.35119
Frank, Rupert L.; Laptev, Ari; Molchanov, Stanislav
5
2008
Lieb-Thirring inequalities on the half-line with critical exponent. Zbl 1147.35020
Ekholm, Tomas; Frank, Rupert L.
5
2008
Remarks about Hardy inequalities on metric trees. Zbl 1175.26035
Ekholm, Tomas; Frank, Rupert L.; Kovařík, Hynek
3
2008
...and 13 more Documents
all top 5

Cited by 1,149 Authors

69 Frank, Rupert L.
28 Seiringer, Robert
19 Lieb, Elliott H.
16 Hainzl, Christian
16 Wei, Juncheng
13 Laptev, Ari
13 Squassina, Marco
12 Lu, Guozhen
12 Solovej, Jan Philip
11 Abdellaoui, Boumediene
11 Ambrosio, Vincenzo
11 Cuenin, Jean-Claude
11 Keller, Matthias
11 Lewin, Mathieu
11 Phan Thành Nam
11 Simon, Barry
10 Kovařík, Hynek
10 Nguyễn Văn Hoàng
10 Peral Alonso, Ireneo
9 Fournais, Søren
9 Hong, Younghun
9 Kachmar, Ayman
8 Berta, Mario
8 Christiansen, Jacob Stordal
8 Esfahani, Amin
8 Exner, Pavel
8 González, María del Mar
8 Lenz, Daniel H.
8 Liu, Weiming
8 Lotoreichik, Vladimir
8 Niu, Miaomiao
8 Sabin, Julien
8 Suragan, Durvudkhan
8 Tang, Zhongwei
8 Tomamichel, Marco
7 Chen, Lu
7 Choi, Woocheol
7 Hansmann, Marcel
7 Lundholm, Douglas
7 Ozawa, Tohru
7 Rougerie, Nicolas
7 Sire, Yannick
7 Stefanov, Atanas G.
7 Topaloglu, Ihsan
7 Valdinoci, Enrico
7 Zinchenko, Maxim
6 Bellazzini, Jacopo
6 Bez, Neal
6 Correggi, Michele
6 Dinh, Van Duong
6 Dipierro, Serena
6 Filippas, Stathis
6 Hua, Bobo
6 Huang, Xueping
6 Laugesen, Richard Snyder
6 Lenzmann, Enno
6 Long, Wei
6 Miyagaki, Olimpio Hiroshi
6 Niu, Pengcheng
6 Oliveira e Silva, Diogo
6 Ruzhansky, Michael V.
6 Siedentop, Heinz Karl Heinrich
6 Tertikas, Achilles
6 Wilde, Mark M.
6 Yang, Jianfu
5 Alama, Stan
5 Alves, Claudianor Oliveira
5 Ao, Weiwei
5 Barrios Barrera, Begoña
5 Brasco, Lorenzo
5 Bronsard, Lia
5 Carlen, Eric Anders
5 Chen, Guoyuan
5 Cinti, Eleonora
5 Ekholm, Tomas
5 Fall, Mouhamed Moustapha
5 Georgiev, Vladimir S.
5 Grubb, Gerd
5 Kim, Seunghyeok
5 Knüpfer, Hans
5 Korotyaev, Evgeny L.
5 Lee, Sanghyuk
5 Loss, Michael
5 Medina, Maria
5 Musina, Roberta
5 Primo, Ana R. M.
5 Psaradakis, Georgios
5 Rohleder, Jonathan
5 Safronov, Oleg
5 Schmidt, Marcel
5 Siudeja, Bartłomiej Andrzej
5 Tao, Chunxia
5 Torres Ledesma, César Enrique
5 Visciglia, Nicola
5 Watanabe, Shuji
5 Weidl, Timo
5 Wojciechowski, Radosław Krzysztof
5 Xiang, Changlin
5 Yang, Hui
5 Zhang, An
...and 1,049 more Authors
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Cited in 203 Serials

79 Journal of Mathematical Physics
60 Calculus of Variations and Partial Differential Equations
52 Communications in Mathematical Physics
49 Journal of Functional Analysis
44 Journal of Mathematical Analysis and Applications
39 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
35 Annales Henri Poincaré
33 Journal of Differential Equations
30 Letters in Mathematical Physics
29 Advances in Mathematics
24 Discrete and Continuous Dynamical Systems
23 Transactions of the American Mathematical Society
22 Communications on Pure and Applied Analysis
18 Archive for Rational Mechanics and Analysis
16 Proceedings of the American Mathematical Society
16 SIAM Journal on Mathematical Analysis
15 Potential Analysis
15 Journal of Spectral Theory
14 Communications in Contemporary Mathematics
13 Complex Variables and Elliptic Equations
12 Reviews in Mathematical Physics
12 Integral Equations and Operator Theory
11 Nonlinearity
11 Mathematische Annalen
11 Journal de Mathématiques Pures et Appliquées. Neuvième Série
11 Advanced Nonlinear Studies
10 Communications in Partial Differential Equations
10 Bulletin of Mathematical Sciences
9 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire
9 The Journal of Geometric Analysis
9 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics
8 ZAMP. Zeitschrift für angewandte Mathematik und Physik
8 Revista Matemática Iberoamericana
8 NoDEA. Nonlinear Differential Equations and Applications
8 Journal of High Energy Physics
8 Journal of Physics A: Mathematical and Theoretical
7 Journal d’Analyse Mathématique
7 Annali di Matematica Pura ed Applicata. Serie Quarta
7 Linear Algebra and its Applications
7 Mathematical Inequalities & Applications
7 Journal of the European Mathematical Society (JEMS)
6 Applicable Analysis
6 Reports on Mathematical Physics
5 Journal of Statistical Physics
5 Mathematische Nachrichten
5 Mathematische Zeitschrift
5 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni
5 Electronic Journal of Differential Equations (EJDE)
5 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations
5 Mathematical Physics, Analysis and Geometry
5 Comptes Rendus. Mathématique. Académie des Sciences, Paris
5 Advances in Nonlinear Analysis
4 Israel Journal of Mathematics
4 Mathematical Methods in the Applied Sciences
4 Journal für die Reine und Angewandte Mathematik
4 Forum Mathematicum
4 Journal of Dynamics and Differential Equations
4 St. Petersburg Mathematical Journal
4 The Journal of Fourier Analysis and Applications
4 Journal of Evolution Equations
4 Milan Journal of Mathematics
4 Journal of Fixed Point Theory and Applications
4 Science China. Mathematics
4 Séminaire Laurent Schwartz. EDP et Applications
3 Archiv der Mathematik
3 Duke Mathematical Journal
3 Illinois Journal of Mathematics
3 Journal of Computational and Applied Mathematics
3 Constructive Approximation
3 Applied Mathematics Letters
3 Stochastic Processes and their Applications
3 Topological Methods in Nonlinear Analysis
3 Acta Mathematica Sinica. English Series
3 Proceedings of the Steklov Institute of Mathematics
3 Complex Analysis and Operator Theory
3 Discrete and Continuous Dynamical Systems. Series S
3 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM
3 Analysis and Mathematical Physics
3 Forum of Mathematics, Sigma
2 Communications on Pure and Applied Mathematics
2 Journal of Computational Physics
2 Russian Mathematical Surveys
2 Annales de l’Institut Fourier
2 The Annals of Probability
2 Applied Mathematics and Computation
2 Funkcialaj Ekvacioj. Serio Internacia
2 Indiana University Mathematics Journal
2 Journal of the London Mathematical Society. Second Series
2 Manuscripta Mathematica
2 Pacific Journal of Mathematics
2 Annals of Global Analysis and Geometry
2 Applied Numerical Mathematics
2 Journal of the American Mathematical Society
2 Integral Transforms and Special Functions
2 Revista Matemática Complutense
2 Annals of Mathematics. Second Series
2 Advances in Calculus of Variations
2 Analysis & PDE
2 São Paulo Journal of Mathematical Sciences
2 Journal of Pseudo-Differential Operators and Applications
...and 103 more Serials
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Cited in 50 Fields

724 Partial differential equations (35-XX)
271 Quantum theory (81-XX)
202 Operator theory (47-XX)
141 Functional analysis (46-XX)
112 Real functions (26-XX)
102 Statistical mechanics, structure of matter (82-XX)
84 Calculus of variations and optimal control; optimization (49-XX)
59 Global analysis, analysis on manifolds (58-XX)
53 Harmonic analysis on Euclidean spaces (42-XX)
49 Information and communication theory, circuits (94-XX)
46 Probability theory and stochastic processes (60-XX)
45 Integral equations (45-XX)
42 Differential geometry (53-XX)
36 Ordinary differential equations (34-XX)
33 Potential theory (31-XX)
28 Combinatorics (05-XX)
23 Difference and functional equations (39-XX)
15 Linear and multilinear algebra; matrix theory (15-XX)
15 Numerical analysis (65-XX)
13 Optics, electromagnetic theory (78-XX)
12 Fluid mechanics (76-XX)
11 Topological groups, Lie groups (22-XX)
11 Dynamical systems and ergodic theory (37-XX)
11 Abstract harmonic analysis (43-XX)
10 Several complex variables and analytic spaces (32-XX)
9 Relativity and gravitational theory (83-XX)
8 Special functions (33-XX)
7 Measure and integration (28-XX)
7 Convex and discrete geometry (52-XX)
7 Mechanics of particles and systems (70-XX)
7 Astronomy and astrophysics (85-XX)
6 Functions of a complex variable (30-XX)
5 Mechanics of deformable solids (74-XX)
4 Number theory (11-XX)
4 Integral transforms, operational calculus (44-XX)
4 Manifolds and cell complexes (57-XX)
3 Algebraic geometry (14-XX)
3 Nonassociative rings and algebras (17-XX)
3 Group theory and generalizations (20-XX)
3 Geometry (51-XX)
3 Statistics (62-XX)
2 General and overarching topics; collections (00-XX)
2 History and biography (01-XX)
2 Approximations and expansions (41-XX)
2 Computer science (68-XX)
2 Biology and other natural sciences (92-XX)
1 Sequences, series, summability (40-XX)
1 Algebraic topology (55-XX)
1 Classical thermodynamics, heat transfer (80-XX)
1 Operations research, mathematical programming (90-XX)

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