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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
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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

Publications by Year

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 1307.35315
Frank, Rupert L.; Lenzmann, Enno
182
2013
Uniqueness of radial solutions for the fractional Laplacian. Zbl 1365.35206
Frank, Rupert L.; Lenzmann, Enno; Silvestre, Luis
178
2016
Nonlinear ground state representations and sharp Hardy inequalities. Zbl 1189.26031
Frank, Rupert L.; Seiringer, Robert
153
2008
Hardy-Lieb-Thirring inequalities for fractional Schrödinger operators. Zbl 1202.35146
Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert
133
2008
Sharp constants in several inequalities on the Heisenberg group. Zbl 1252.42023
Frank, Rupert L.; Lieb, Elliott H.
70
2012
Monotonicity of a relative Rényi entropy. Zbl 1350.94020
Frank, Rupert L.; Lieb, Elliott H.
57
2013
Eigenvalue bounds for Schrödinger operators with complex potentials. Zbl 1228.35158
Frank, Rupert L.
54
2011
Inversion positivity and the sharp Hardy-Littlewood-Sobolev inequality. Zbl 1204.39024
Frank, Rupert L.; Lieb, Elliott H.
51
2010
Intrinsic metrics for non-local symmetric Dirichlet forms and applications to spectral theory. Zbl 1304.60081
Frank, Rupert L.; Lenz, Daniel; Wingert, Daniel
47
2014
Lieb-Thirring inequalities for Schrödinger operators with complex-valued potentials. Zbl 1160.81382
Frank, Rupert L.; Laptev, Ari; Lieb, Elliott H.; Seiringer, Robert
44
2006
Maximizers for Gagliardo-Nirenberg inequalities and related non-local problems. Zbl 1320.46026
Bellazzini, Jacopo; Frank, Rupert L.; Visciglia, Nicola
36
2014
A new, rearrangement-free proof of the sharp Hardy-Littlewood-Sobolev inequality. Zbl 1297.39023
Frank, 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 1173.26011
Benguria, Rafael D.; Frank, Rupert L.; Loss, Michael
36
2008
Eigenvalue bounds for Schrödinger operators with complex potentials. III. Zbl 1390.35204
Frank, Rupert L.
35
2018
Restriction theorems for orthonormal functions, Strichartz inequalities, and uniform Sobolev estimates. Zbl 1388.42018
Frank, Rupert L.; Sabin, Julien
35
2017
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.
31
2015
Eigenvalue bounds for Schrödinger operators with complex potentials II. Zbl 1386.35061
Frank, Rupert L.; Simon, Barry
28
2017
Microscopic derivation of Ginzburg-Landau theory. Zbl 1251.35156
Frank, Rupert L.; Hainzl, Christian; Seiringer, Robert; Solovej, Jan Philip
28
2012
The critical temperature for the BCS equation at weak coupling. Zbl 1137.82025
Frank, Rupert L.; Hainzl, Christian; Naboko, Serguei; Seiringer, Robert
28
2007
An extension problem for the CR fractional Laplacian. Zbl 1304.35747
Frank, Rupert L.; del Mar González, María; Monticelli, Dario D.; Tan, Jinggang
27
2015
Refined semiclassical asymptotics for fractional powers of the Laplace operator. Zbl 1337.35163
Frank, Rupert L.; Geisinger, Leander
27
2016
On Lieb-Thirring inequalities for Schrödinger operators with virtual level. Zbl 1106.81039
Ekholm, T.; Frank, R. L.
26
2006
A simple proof of Hardy-Lieb-Thirring inequalities. Zbl 1184.35121
Frank, Rupert L.
25
2009
On the number of eigenvalues of Schrödinger operators with complex potentials. Zbl 1358.35074
Frank, Rupert L.; Laptev, Ari; Safronov, Oleg
24
2016
Remainder terms in the fractional Sobolev inequality. Zbl 1296.46032
Chen, Shibing; Frank, Rupert L.; Weth, Tobias
23
2013
Strichartz inequality for orthonormal functions. Zbl 1307.35245
Frank, Rupert L.; Lewin, Mathieu; Lieb, Elliott H.; Seiringer, Robert
22
2014
Sharp fractional Hardy inequalities in half-spaces. Zbl 1185.26044
Frank, Rupert L.; Seiringer, Robert
21
2010
Stability estimates for the lowest eigenvalue of a Schrödinger operator. Zbl 1291.35145
Carlen, Eric A.; Frank, Rupert L.; Lieb, Elliott H.
20
2014
A positive density analogue of the Lieb-Thirring inequality. Zbl 1260.35088
Frank, Rupert L.; Lewin, Mathieu; Lieb, Elliott H.; Seiringer, Robert
19
2013
Hardy-Sobolev-Maz’ya inequalities for arbitrary domains. Zbl 1233.49023
Frank, Rupert L.; Loss, Michael
17
2012
Fractional Hardy-Sobolev-Maz’ya inequality for domains. Zbl 1273.26025
Dyda, Bartłomiej; Frank, Rupert L.
17
2012
Classification of positive singular solutions to a nonlinear biharmonic equation with critical exponent. Zbl 1421.35150
Frank, Rupert L.; König, Tobias
16
2019
Derivation of an effective evolution equation for a strongly coupled polaron. Zbl 1365.35130
Frank, Rupert L.; Zhou, Gang
16
2017
Singular spectrum for radial trees. Zbl 1177.05069
Breuer, Jonathan; Frank, Rupert L.
16
2009
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
15
2011
Nonexistence of large nuclei in the liquid drop model. Zbl 1347.49069
Frank, Rupert L.; Killip, Rowan; Phan Thành Nam
15
2016
The ionization conjecture in Thomas-Fermi-Dirac-von Weizsäcker theory. Zbl 1386.49063
Frank, 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 1158.35021
Frank, Rupert L.; Simon, Barry; Weidl, Timo
14
2008
Lieb-Thirring inequality for a model of particles with point interactions. Zbl 1278.81061
Frank, Rupert L.; Seiringer, Robert
13
2012
Cwikel’s theorem and the CLR inequality. Zbl 1295.35347
Frank, Rupert L.
13
2014
Dynamics of a strongly coupled polaron. Zbl 1297.35202
Frank, Rupert L.; Schlein, Benjamin
13
2014
Maximizers for the Stein-Tomas inequality. Zbl 1357.42023
Frank, Rupert L.; Lieb, Elliott H.; Sabin, Julien
13
2016
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
Pólya’s conjecture in the presence of a constant magnetic field. Zbl 1179.35205
Frank, 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 1420.49040
Frank, Rupert; Lieb, Elliott H.
12
2018
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
12
2007
The ground state energy of heavy atoms: Relativistic lowering of the leading energy correction. Zbl 1162.81037
Frank, Rupert L.; Siedentop, Heinz; Warzel, Simone
11
2008
Some operator and trace function convexity theorems. Zbl 1342.47024
Carlen, Eric A.; Frank, Rupert L.; Lieb, Elliott H.
11
2016
Equivalence of Sobolev inequalities and Lieb-Thirring inequalities. Zbl 1203.81072
Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert
10
2010
Inequalities for quantum divergences and the Audenaert-Datta conjecture. Zbl 1414.81064
Carlen, Eric A.; Frank, Rupert L.; Lieb, Elliott H.
9
2018
Sharp decay estimates for critical Dirac equations. Zbl 1435.35053
Borrelli, William; Frank, Rupert L.
9
2020
On the asymptotic number of edge states for magnetic Schrödinger operators. Zbl 1131.35076
Frank, Rupert L.
9
2007
Binding of polarons and atoms at threshold. Zbl 1250.82046
Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert
9
2012
Eigenvalue estimates for Schrödinger operators on metric trees. Zbl 1237.35157
Ekholm, 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 1229.35157
Frank, Rupert L.; Simon, Barry
9
2011
The energy of heavy atoms according to Brown and Ravenhall: the Scott correction. Zbl 1186.81137
Frank, Rupert L.; Siedentop, Heinz; Warzel, Simone
9
2009
Eigenvalue bounds for the fractional Laplacian: a review. Zbl 1404.35303
Frank, Rupert L.
8
2018
Two-term spectral asymptotics for the Dirichlet Laplacian on a bounded domain. Zbl 1253.47031
Frank, Rupert L.; Geisinger, Leander
8
2011
The external field dependence of the BCS critical temperature. Zbl 1334.82080
Frank, Rupert L.; Hainzl, Christian; Seiringer, Robert; Solovej, Jan Philip
8
2016
Semi-classical analysis of the Laplace operator with Robin boundary conditions. Zbl 1253.35090
Frank, Rupert L.; Geisinger, Leander
8
2012
Extended quantum conditional entropy and quantum uncertainty inequalities. Zbl 1280.81022
Frank, Rupert L.; Lieb, Elliott H.
7
2013
Minimizers for the fractional Sobolev inequality on domains. Zbl 1393.26026
Frank, Rupert L.; Jin, Tianling; Xiong, Jingang
7
2018
Norms of quantum Gaussian multi-mode channels. Zbl 1366.81091
Frank, Rupert L.; Lieb, Elliott H.
7
2017
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
A non-linear adiabatic theorem for the one-dimensional Landau-Pekar equations. Zbl 1445.35128
Frank, Rupert L.; Gang, Zhou
6
2020
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
Multi-component Ginzburg-Landau theory: microscopic derivation and examples. Zbl 1351.82117
Frank, Rupert L.; Lemm, Marius
6
2016
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
Spectral inequalities for Schrödinger operators with surface potentials. Zbl 1170.35486
Frank, Rupert L.; Laptev, Ari
6
2008
Lieb-Thirring inequalities on the half-line with critical exponent. Zbl 1147.35020
Ekholm, Tomas; Frank, Rupert L.
5
2008
Eigenvalue estimates for magnetic Schrödinger operators in domains. Zbl 1186.35119
Frank, Rupert L.; Laptev, Ari; Molchanov, Stanislav
5
2008
The maximal excess charge in Müller density-matrix-functional theory. Zbl 1397.81456
Frank, Rupert L.; Phan Thành Nam; van den Bosch, Hanne
5
2018
Reverse Hardy-Littlewood-Sobolev inequalities. Zbl 1442.35011
Carrillo, 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 1301.35070
Cornean, Horia D.; Fournais, Søren; Frank, Rupert L.; Helffer, Bernard
5
2013
Endpoint resolvent estimates for compact Riemannian manifolds. Zbl 1360.58015
Frank, Rupert L.; Schimmer, Lukas
5
2017
Absolute continuity of the spectrum for periodically modulated leaky wires in \({\mathbb{R}^{3}}\). Zbl 1206.82112
Exner, Pavel; Frank, Rupert L.
5
2007
Number of bound states of Schrödinger operators with matrix-valued potentials. Zbl 1135.35052
Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert
5
2007
Spherical reflection positivity and the Hardy-Littlewood-Sobolev inequality. Zbl 1378.39013
Frank, Rupert L.; Lieb, Elliott H.
5
2011
Weakly coupled bound states of Pauli operators. Zbl 1205.35177
Frank, 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 1142.35374
Frank, Rupert L.
4
2003
Two-term spectral asymptotics for the Dirichlet Laplacian in a Lipschitz domain. Zbl 1467.35107
Frank, Rupert L.; Larson, Simon
4
2020
Equivalence of Sobolev norms involving generalized Hardy operators. Zbl 1470.81033
Frank, Rupert L.; Merz, Konstantin; Siedentop, Heinz
4
2021
Inequalities between Dirichlet and Neumann eigenvalues on the Heisenberg group. Zbl 1198.35161
Frank, Rupert L.; Laptev, Ari
4
2010
Remarks on eigenvalue estimates and semigroup domination. Zbl 1183.81068
Frank, Rupert L.
4
2009
Ground state properties of multi-polaron systems. Zbl 1304.82075
Frank, R. L.; Lieb, E. H.; Seiringer, R.; Thomas, L. E.
4
2014
Entropy and the uncertainty principle. Zbl 1256.81022
Frank, Rupert L.; Lieb, Elliott H.
4
2012
The ground state energy of a polaron in a strong magnetic field. Zbl 1323.82045
Frank, Rupert L.; Geisinger, Leander
4
2015
Kato smoothness and functions of perturbed self-adjoint operators. Zbl 07078811
Frank, Rupert L.; Pushnitski, Alexander
3
2019
Heat kernels of metric trees and applications. Zbl 1278.47048
Frank, Rupert L.; Kovařík, Hynek
3
2013
Remarks about Hardy inequalities on metric trees. Zbl 1175.26035
Ekholm, Tomas; Frank, Rupert L.; Kovařík, Hynek
3
2008
On the spectrum of partially periodic operators. Zbl 1210.35041
Frank, Rupert L.; Shterenberg, Roman G.
3
2007
Classification of solutions of an equation related to a conformal log Sobolev inequality. Zbl 1453.35036
Frank, Rupert L.; König, Tobias; Tang, Hanli
3
2020
Quantum corrections to the Pekar asymptotics of a strongly coupled polaron. Zbl 1467.82092
Frank, Rupert L.; Seiringer, Robert
3
2021
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
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
Spectral cluster bounds for orthonormal systems and oscillatory integral operators in Schatten spaces. Zbl 1373.58015
Frank, Rupert L.; Sabin, Julien
3
2017
The Stein-Tomas inequality in trace ideals. Zbl 1358.35010
Frank, Rupert L.; Sabin, Julien
3
2016
On the tunneling effect for magnetic Schrödinger operators in antidot lattices. Zbl 1157.81309
Frank, Rupert L.
3
2006
Weak perturbations of the \(p\)-Laplacian. Zbl 1322.49076
Ekholm, Tomas; Frank, Rupert L.; Kovařík, Hynek
3
2015
Counting eigenvalues of Schrödinger operators with fast decaying complex potentials. Zbl 07472307
Borichev, Alexander; Frank, Rupert L.; Volberg, Alexander
1
2022
Equivalence of Sobolev norms involving generalized Hardy operators. Zbl 1470.81033
Frank, Rupert L.; Merz, Konstantin; Siedentop, Heinz
4
2021
Quantum corrections to the Pekar asymptotics of a strongly coupled polaron. Zbl 1467.82092
Frank, Rupert L.; Seiringer, Robert
3
2021
Existence and nonexistence in the liquid drop model. Zbl 07414044
Frank, Rupert L.; Nam, Phan Thành
3
2021
The nonlinear Schrödinger equation for orthonormal functions. II: Application to Lieb-Thirring inequalities. Zbl 1465.35015
Frank, Rupert L.; Gontier, David; Lewin, Mathieu
2
2021
The Lieb-Thirring inequality revisited. Zbl 1467.35014
Frank, Rupert L.; Hundertmark, Dirk; Jex, Michal; Nam, Phan Thành
1
2021
Non-degeneracy for the critical Lane-Emden system. Zbl 1464.35097
Frank, Rupert L.; Kim, Seunghyeok; Pistoia, Angela
1
2021
Proof of spherical flocking based on quantitative rearrangement inequalities. Zbl 1478.49020
Frank, Rupert L.; Lieb, Elliott H.
1
2021
Sharp decay estimates for critical Dirac equations. Zbl 1435.35053
Borrelli, William; Frank, Rupert L.
9
2020
A non-linear adiabatic theorem for the one-dimensional Landau-Pekar equations. Zbl 1445.35128
Frank, Rupert L.; Gang, Zhou
6
2020
Two-term spectral asymptotics for the Dirichlet Laplacian in a Lipschitz domain. Zbl 1467.35107
Frank, Rupert L.; Larson, Simon
4
2020
Classification of solutions of an equation related to a conformal log Sobolev inequality. Zbl 1453.35036
Frank, Rupert L.; König, Tobias; Tang, Hanli
3
2020
Proof of the strong Scott conjecture for Chandrasekhar atoms. Zbl 1465.81076
Frank, 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 1479.46029
Carlen, Eric A.; Frank, Rupert L.; Lieb, Elliott H.
1
2020
Liquid drop model for nuclear matter in the dilute limit. Zbl 1439.81090
Emmert, Lukas; Frank, Rupert L.; König, Tobias
1
2020
On the error in the two-term Weyl formula for the Dirichlet Laplacian. Zbl 1458.35142
Frank, Rupert L.; Larson, Simon
1
2020
Classification of positive singular solutions to a nonlinear biharmonic equation with critical exponent. Zbl 1421.35150
Frank, Rupert L.; König, Tobias
16
2019
Reverse Hardy-Littlewood-Sobolev inequalities. Zbl 1442.35011
Carrillo, José A.; Delgadino, Matías G.; Dolbeault, Jean; Frank, Rupert L.; Hoffmann, Franca
5
2019
Kato smoothness and functions of perturbed self-adjoint operators. Zbl 07078811
Frank, Rupert L.; Pushnitski, Alexander
3
2019
Singular solutions to a semilinear biharmonic equation with a general critical nonlinearity. Zbl 1454.35102
Frank, Rupert L.; König, Tobias
2
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.
2
2019
Non-spherical equilibrium shapes in the liquid drop model. Zbl 1416.81223
Frank, Rupert L.
1
2019
Eigenvalue bounds for Schrödinger operators with complex potentials. III. Zbl 1390.35204
Frank, Rupert L.
35
2018
The ionization conjecture in Thomas-Fermi-Dirac-von Weizsäcker theory. Zbl 1386.49063
Frank, 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 1420.49040
Frank, Rupert; Lieb, Elliott H.
12
2018
Inequalities for quantum divergences and the Audenaert-Datta conjecture. Zbl 1414.81064
Carlen, Eric A.; Frank, Rupert L.; Lieb, Elliott H.
9
2018
Eigenvalue bounds for the fractional Laplacian: a review. Zbl 1404.35303
Frank, Rupert L.
8
2018
Minimizers for the fractional Sobolev inequality on domains. Zbl 1393.26026
Frank, Rupert L.; Jin, Tianling; Xiong, Jingang
7
2018
The maximal excess charge in Müller density-matrix-functional theory. Zbl 1397.81456
Frank, Rupert L.; Phan Thành Nam; van den Bosch, Hanne
5
2018
Extremizers for the Airy-Strichartz inequality. Zbl 1406.35354
Frank, Rupert L.; Sabin, Julien
2
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
Restriction theorems for orthonormal functions, Strichartz inequalities, and uniform Sobolev estimates. Zbl 1388.42018
Frank, Rupert L.; Sabin, Julien
35
2017
Eigenvalue bounds for Schrödinger operators with complex potentials II. Zbl 1386.35061
Frank, Rupert L.; Simon, Barry
28
2017
Derivation of an effective evolution equation for a strongly coupled polaron. Zbl 1365.35130
Frank, Rupert L.; Zhou, Gang
16
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
5
2017
Spectral cluster bounds for orthonormal systems and oscillatory integral operators in Schatten spaces. Zbl 1373.58015
Frank, Rupert L.; Sabin, Julien
3
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
2
2017
Uniqueness of radial solutions for the fractional Laplacian. Zbl 1365.35206
Frank, Rupert L.; Lenzmann, Enno; Silvestre, Luis
178
2016
Refined semiclassical asymptotics for fractional powers of the Laplace operator. Zbl 1337.35163
Frank, Rupert L.; Geisinger, Leander
27
2016
On the number of eigenvalues of Schrödinger operators with complex potentials. Zbl 1358.35074
Frank, Rupert L.; Laptev, Ari; Safronov, Oleg
24
2016
Nonexistence of large nuclei in the liquid drop model. Zbl 1347.49069
Frank, Rupert L.; Killip, Rowan; Phan Thành Nam
15
2016
Maximizers for the Stein-Tomas inequality. Zbl 1357.42023
Frank, Rupert L.; Lieb, Elliott H.; Sabin, Julien
13
2016
Some operator and trace function convexity theorems. Zbl 1342.47024
Carlen, Eric A.; Frank, Rupert L.; Lieb, Elliott H.
11
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
6
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.
31
2015
An extension problem for the CR fractional Laplacian. Zbl 1304.35747
Frank, Rupert L.; del Mar González, María; Monticelli, Dario D.; Tan, Jinggang
27
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
47
2014
Maximizers for Gagliardo-Nirenberg inequalities and related non-local problems. Zbl 1320.46026
Bellazzini, Jacopo; Frank, Rupert L.; Visciglia, Nicola
36
2014
Strichartz inequality for orthonormal functions. Zbl 1307.35245
Frank, Rupert L.; Lewin, Mathieu; Lieb, Elliott H.; Seiringer, Robert
22
2014
Stability estimates for the lowest eigenvalue of a Schrödinger operator. Zbl 1291.35145
Carlen, Eric A.; Frank, Rupert L.; Lieb, Elliott H.
20
2014
Cwikel’s theorem and the CLR inequality. Zbl 1295.35347
Frank, Rupert L.
13
2014
Dynamics of a strongly coupled polaron. Zbl 1297.35202
Frank, Rupert L.; Schlein, Benjamin
13
2014
Ground state properties of multi-polaron systems. Zbl 1304.82075
Frank, R. L.; Lieb, E. H.; Seiringer, R.; Thomas, L. E.
4
2014
Existence of ground states for negative ions at the binding threshold. Zbl 1302.81099
Bellazzini, Jacopo; Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert
3
2014
Uniqueness of non-linear ground states for fractional Laplacians in \(\mathbb{R}\). Zbl 1307.35315
Frank, Rupert L.; Lenzmann, Enno
182
2013
Monotonicity of a relative Rényi entropy. Zbl 1350.94020
Frank, Rupert L.; Lieb, Elliott H.
57
2013
Remainder terms in the fractional Sobolev inequality. Zbl 1296.46032
Chen, Shibing; Frank, Rupert L.; Weth, Tobias
23
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
Extended quantum conditional entropy and quantum uncertainty inequalities. Zbl 1280.81022
Frank, Rupert L.; Lieb, Elliott H.
7
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
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
2
2013
Sharp constants in several inequalities on the Heisenberg group. Zbl 1252.42023
Frank, Rupert L.; Lieb, Elliott H.
70
2012
A new, rearrangement-free proof of the sharp Hardy-Littlewood-Sobolev inequality. Zbl 1297.39023
Frank, Rupert L.; Lieb, Elliott H.
36
2012
Microscopic derivation of Ginzburg-Landau theory. Zbl 1251.35156
Frank, Rupert L.; Hainzl, Christian; Seiringer, Robert; Solovej, Jan Philip
28
2012
Hardy-Sobolev-Maz’ya inequalities for arbitrary domains. Zbl 1233.49023
Frank, Rupert L.; Loss, Michael
17
2012
Fractional Hardy-Sobolev-Maz’ya inequality for domains. Zbl 1273.26025
Dyda, Bartłomiej; Frank, Rupert L.
17
2012
Lieb-Thirring inequality for a model of particles with point interactions. Zbl 1278.81061
Frank, Rupert L.; Seiringer, Robert
13
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
8
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.
54
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
15
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
Eigenvalue estimates for Schrödinger operators on metric trees. Zbl 1237.35157
Ekholm, 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 1229.35157
Frank, Rupert L.; Simon, Barry
9
2011
Two-term spectral asymptotics for the Dirichlet Laplacian on a bounded domain. Zbl 1253.47031
Frank, Rupert L.; Geisinger, Leander
8
2011
Spherical reflection positivity and the Hardy-Littlewood-Sobolev inequality. Zbl 1378.39013
Frank, Rupert L.; Lieb, Elliott H.
5
2011
Weakly coupled bound states of Pauli operators. Zbl 1205.35177
Frank, Rupert L.; Morozov, Sergey; Vugalter, Semjon
5
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.
51
2010
Sharp fractional Hardy inequalities in half-spaces. Zbl 1185.26044
Frank, Rupert L.; Seiringer, Robert
21
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
4
2010
A simple proof of Hardy-Lieb-Thirring inequalities. Zbl 1184.35121
Frank, Rupert L.
25
2009
Singular spectrum for radial trees. Zbl 1177.05069
Breuer, Jonathan; Frank, Rupert L.
16
2009
Pólya’s conjecture in the presence of a constant magnetic field. Zbl 1179.35205
Frank, Rupert L.; Loss, Michael; Weidl, Timo
13
2009
...and 26 more Documents
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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
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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. Series A: Theory and Methods
47 Journal of Mathematical Analysis and Applications
41 Journal of Differential Equations
38 Annales Henri Poincaré
35 Advances in Mathematics
31 Letters in Mathematical Physics
29 Communications on Pure and Applied Analysis
26 Discrete and Continuous Dynamical Systems
25 Transactions of the American Mathematical Society
23 Journal of Spectral Theory
19 Archive for Rational Mechanics and Analysis
17 Proceedings of the American Mathematical Society
17 SIAM Journal on Mathematical Analysis
17 Communications in Contemporary Mathematics
16 Nonlinearity
16 Advanced Nonlinear Studies
15 Potential Analysis
14 Reviews in Mathematical Physics
14 Journal de Mathématiques Pures et Appliquées. Neuvième Série
14 Complex Variables and Elliptic Equations
13 Integral Equations and Operator Theory
13 Communications in Partial Differential Equations
12 The Journal of Geometric Analysis
11 Mathematische Annalen
10 ZAMP. Zeitschrift für angewandte Mathematik und Physik
10 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics
10 NoDEA. Nonlinear Differential Equations and Applications
10 Bulletin of Mathematical Sciences
9 Applicable Analysis
9 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire
8 Journal d’Analyse Mathématique
8 Revista Matemática Iberoamericana
8 Linear Algebra and its Applications
8 Journal of High Energy Physics
8 Comptes Rendus. Mathématique. Académie des Sciences, Paris
8 Journal of Physics A: Mathematical and Theoretical
8 Discrete and Continuous Dynamical Systems. Series S
7 Reports on Mathematical Physics
7 Annali di Matematica Pura ed Applicata. Serie Quarta
7 Mathematische Zeitschrift
7 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations
7 Mathematical Physics, Analysis and Geometry
7 Mathematical Inequalities & Applications
7 Journal of the European Mathematical Society (JEMS)
6 Journal of Statistical Physics
6 Boundary Value Problems
6 Advances in Nonlinear Analysis
5 Journal für die Reine und Angewandte Mathematik
5 Mathematische Nachrichten
5 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni
5 Journal of Dynamics and Differential Equations
5 Electronic Journal of Differential Equations (EJDE)
5 The Journal of Fourier Analysis and Applications
5 Séminaire Laurent Schwartz. EDP et Applications
4 Israel Journal of Mathematics
4 Mathematical Methods in the Applied Sciences
4 Functional Analysis and its Applications
4 Forum Mathematicum
4 St. Petersburg Mathematical Journal
4 Revista Matemática Complutense
4 Journal of Evolution Equations
4 Milan Journal of Mathematics
4 Journal of Fixed Point Theory and Applications
4 Science China. Mathematics
4 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM
3 Journal of Computational Physics
3 Archiv der Mathematik
3 Duke Mathematical Journal
3 Illinois Journal of Mathematics
3 Indiana University Mathematics Journal
3 Journal of Computational and Applied Mathematics
3 Manuscripta Mathematica
3 Constructive Approximation
3 Applied Mathematics Letters
3 Stochastic Processes and their Applications
3 Topological Methods in Nonlinear Analysis
3 Fractional Calculus & Applied Analysis
3 Acta Mathematica Sinica. English Series
3 Proceedings of the Steklov Institute of Mathematics
3 Complex Analysis and Operator Theory
3 Advances in Calculus of Variations
3 Journal of Pseudo-Differential Operators and Applications
3 Analysis and Mathematical Physics
3 Forum of Mathematics, Sigma
3 Journal de l’École Polytechnique – Mathématiques
3 AIMS Mathematics
3 Annales Henri Lebesgue
2 Communications on Pure and Applied Mathematics
2 International Journal of Theoretical 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 Journal of the London Mathematical Society. Second Series
2 Pacific Journal of Mathematics
...and 128 more Serials
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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)

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