CaltechAUTHORS
  A Caltech Library Service

Items where Person is "Frank-R-L"

Up a level
Export as [feed] Atom [feed] RSS 1.0 [feed] RSS 2.0
Group by: Date | Item Type | First Author | No Grouping
Jump to: 2019 | 2018 | 2017 | 2016 | 2015 | 2014 | 2013 | 2012 | 2011 | 2010 | 2009 | 2008 | 2007 | 2006
Number of items: 123.

2019

Frank, Rupert L. and Pushnitski, Alexander (2019) Kato smoothness and functions of perturbed self-adjoint operators. Advances in Mathematics, 351 . pp. 343-387. ISSN 0001-8708. http://resolver.caltech.edu/CaltechAUTHORS:20190520-102006314

Frank, Rupert L. (2019) Non-spherical equilibrium shapes in the liquid drop model. Journal of Mathematical Physics, 60 (7). Art. No. 071506. ISSN 0022-2488. http://resolver.caltech.edu/CaltechAUTHORS:20190520-132849818

Frank, Rupert L. and Lieb, Elliott H. (2019) Periodic energy minimizers for a one-dimensional liquid drop model. Letters in Mathematical Physics . ISSN 0377-9017 . (In Press) http://resolver.caltech.edu/CaltechAUTHORS:20190429-123953827

Frank, R. L. and Laptev, A. (2019) Bound on the number of negative eigenvalues of two-dimensional Schrödinger operators on domains. St. Petersburg Mathematical Journal, 30 (3). pp. 573-589. ISSN 1061-0022. http://resolver.caltech.edu/CaltechAUTHORS:20180604-111721567

Frank, Rupert L. and König, Tobias (2019) Singular solutions to a semilinear biharmonic equation with a general critical nonlinearity. . (Unpublished) http://resolver.caltech.edu/CaltechAUTHORS:20190520-133342030

Carlen, Eric A. and Frank, Rupert L. and Lieb, Elliott H. (2019) Inequalities that sharpen the triangle inequality for sums of N functions in L^p. . (Unpublished) http://resolver.caltech.edu/CaltechAUTHORS:20190520-133118107

Frank, Rupert L. and Larson, Simon (2019) Two-term spectral asymptotics for the Dirichlet Laplacian in a Lipschitz domain. . (Unpublished) http://resolver.caltech.edu/CaltechAUTHORS:20190520-133710218

Frank, Rupert L. and Pushnitski, Alexander (2019) Schatten class conditions for functions of Schrödinger operators. . (Unpublished) http://resolver.caltech.edu/CaltechAUTHORS:20190520-133945892

2018

Frank, Rupert L. and Sabin, Julien (2018) Extremizers for the Airy–Strichartz inequality. Mathematische Annalen, 372 (3-4). pp. 1121-1166. ISSN 0025-5831. http://resolver.caltech.edu/CaltechAUTHORS:20180604-091720191

Carlen, Eric A. and Frank, Rupert L. and Lieb, Elliott H. (2018) Inequalities for quantum divergences and the Audenaert–Datta conjecture. Journal of Physics A: Mathematical and Theoretical, 51 (48). Art. No. 483001. ISSN 1751-8113. http://resolver.caltech.edu/CaltechAUTHORS:20181106-123858044

Frank, Rupert L. and Nam, Phan Thành and Van Den Bosch, Hanne (2018) A short proof of the ionization conjecture in Müller theory. In: Mathematical Problems in Quantum Physics. Contemporary Mathematics . No.717. American Mathematical Society , Providence, RI, pp. 1-12. ISBN 978-1-4704-3681-0. http://resolver.caltech.edu/CaltechAUTHORS:20190513-100341402

Frank, Rupert L. and König, Tobias (2018) Classification of positive solutions to a nonlinear biharmonic equation with critical exponent. Analysis & PDE, 12 (4). pp. 1101-1113. ISSN 1948-206X. http://resolver.caltech.edu/CaltechAUTHORS:20180604-112112515

Borrelli, William and Frank, Rupert L. (2018) Sharp decay estimates for critical Dirac equations. . (Unpublished) http://resolver.caltech.edu/CaltechAUTHORS:20190520-135426746

Frank, Rupert L. and Nam, Phan Thành and Van Den Bosch, Hanne (2018) The maximal excess charge in Müller density-matrix-functional theory. Annales Henri Poincaré, 19 (9). pp. 2839-2867. ISSN 1424-0637. http://resolver.caltech.edu/CaltechAUTHORS:20170428-155623144

Emmert, Lukas and Frank, Rupert L. and König, Tobias (2018) Liquid Drop Model for Nuclear Matter in the Dilute Limit. . (Unpublished) http://resolver.caltech.edu/CaltechAUTHORS:20190520-135621604

Frank, Rupert L. and Merz, Konstantin and Siedentop, Heinz (2018) Equivalence of Sobolev norms involving generalized Hardy operators. . (Unpublished) http://resolver.caltech.edu/CaltechAUTHORS:20190520-135826551

Carlen, Eric A. and Frank, Rupert L. and Ivanisvili, Paata et al. (2018) Inequalities for L^p-norms that sharpen the triangle inequality and complement Hanner's Inequality. . (Unpublished) http://resolver.caltech.edu/CaltechAUTHORS:20190520-141054764

Frank, Rupert L. and Jin, Tianling and Xiong, Jingang (2018) Minimizers for the fractional Sobolev inequality on domains. Calculus of Variations and Partial Differential Equations, 57 (2). Art. No. 43. ISSN 0944-2669. http://resolver.caltech.edu/CaltechAUTHORS:20180221-110808137

Dolbeault, Jean and Frank, Rupert L. and Hoffmann, Franca (2018) Reverse Hardy-Littlewood-Sobolev inequalities. . (Submitted) http://resolver.caltech.edu/CaltechAUTHORS:20180604-111058055

Frank, Rupert L. and Nam, Phan Thành and Van Den Bosch, Hanne (2018) The ionization conjecture in Thomas-Fermi-Dirac-von Weizsäcker theory. Communications on Pure and Applied Mathematics, 71 (3). pp. 577-614. ISSN 0010-3640. http://resolver.caltech.edu/CaltechAUTHORS:20170501-083145482

Frank, Rupert L. and Lieb, Elliott H. (2018) A "Liquid-Solid" Phase Transition in a Simple Model for Swarming, Based on the "No Flat-Spots" Theorem for Subharmonic Functions. Indiana University Mathematics Journal, 67 (4). pp. 1547-1569. ISSN 0022-2518. http://resolver.caltech.edu/CaltechAUTHORS:20180912-155642789

2017

Frank, Rupert L. and Sabin, Julien (2017) Restriction theorems for orthonormal functions, Strichartz inequalities, and uniform Sobolev estimates. American Journal of Mathematics, 139 (6). pp. 1649-1691. ISSN 0002-9327. http://resolver.caltech.edu/CaltechAUTHORS:20170501-160524071

Frank, Rupert L. and Simon, Barry (2017) Eigenvalue bounds for Schrödinger operators with complex potentials. II. Journal of Spectral Theory, 7 (3). pp. 633-658. ISSN 1664-039X. http://resolver.caltech.edu/CaltechAUTHORS:20170502-082840587

Frank, Rupert L. and Sabin, Julien (2017) Spectral cluster bounds for orthonormal systems and oscillatory integral operators in Schatten spaces. Advances in Mathematics, 317 . pp. 157-192. ISSN 0001-8708. http://resolver.caltech.edu/CaltechAUTHORS:20170428-155217715

Frank, Rupert L. (2017) Eigenvalue bounds for Schrödinger operators with complex potentials. III. Transactions of the American Mathematical Society, 370 . pp. 219-240. ISSN 0002-9947. http://resolver.caltech.edu/CaltechAUTHORS:20170502-081943954

Frank, Rupert L. and Hainzl, Christian and Langmann, Edwin (2017) The BCS critical temperature in a weak homogeneous magnetic field. . (Submitted) http://resolver.caltech.edu/CaltechAUTHORS:20180604-112611120

Frank, Rupert L. and Lieb, Elliott H. (2017) Norms of quantum Gaussian multi-mode channels. Journal of Mathematical Physics, 58 (6). Art. No. 062204. ISSN 0022-2488. http://resolver.caltech.edu/CaltechAUTHORS:20170720-090957243

Frank, Rupert L. and Schimmer, Lukas (2017) Endpoint resolvent estimates for compact Riemannian manifolds. Journal of Functional Analysis, 272 (9). pp. 3904-3918. ISSN 0022-1236. http://resolver.caltech.edu/CaltechAUTHORS:20170427-140719939

Frank, Rupert L. (2017) Eigenvalues of Schrödinger operators with complex surface potentials. In: Functional Analysis and Operator Theory for Quantum Physics: The Pavel Exner Anniversary Volume. EMS series of congress reports. , Zürich, pp. 245-259. ISBN 978-3-03719-175-0. http://resolver.caltech.edu/CaltechAUTHORS:20170501-155923176

Frank, Rupert L. and Lemm, Marius and Simon, Barry (2017) Condensation of fermion pairs in a domain. Calculus of Variations and Partial Differential Equations, 56 . Art. No. 54. ISSN 0944-2669. http://resolver.caltech.edu/CaltechAUTHORS:20170428-160716872

Behrndt, Jussi and Frank, Rupert L. and Kühn, Christian et al. (2017) Spectral Theory for Schrödinger Operators with δ-Interactions Supported on Curves in R^3. Annales Henri Poincaré, 18 (4). pp. 1305-1347. ISSN 1424-0637. http://resolver.caltech.edu/CaltechAUTHORS:20170417-074808881

Frank, Rupert L. and Méhats, Florian and Sparber, Christof (2017) Averaging of nonlinear Schrödinger equations with strong magnetic confinement. Communications in Mathematical Sciences, 15 (7). pp. 1933-1945. ISSN 1539-6746. http://resolver.caltech.edu/CaltechAUTHORS:20170428-154120889

Frank, Rupert L. and Zhou, Gang (2017) Derivation of an effective evolution equation for a strongly coupled polaron. Analysis & PDE, 10 (2). pp. 379-422. ISSN 2157-5045. http://resolver.caltech.edu/CaltechAUTHORS:20170427-075023929

Frank, Rupert L. (2017) Eigenvalue bounds for the fractional Laplacian: A review. In: Recent Developments in Nonlocal Theory. De Gruyter , Berlin, pp. 210-235. ISBN 9783110571561. http://resolver.caltech.edu/CaltechAUTHORS:20170501-092157290

2016

Frank, Rupert L. and Laptev, Ari and Safronov, Oleg (2016) On the number of eigenvalues of Schrödinger operators with complex potentials. Journal of the London Mathematical Society, 94 (2). pp. 377-390. ISSN 0024-6107. http://resolver.caltech.edu/CaltechAUTHORS:20161128-153447509

Frank, Rupert L. and Lemm, Marius (2016) Multi-Component Ginzburg-Landau Theory: Microscopic Derivation and Examples. Annales Henri Poincaré, 17 (9). pp. 2285-2340. ISSN 1424-0637. http://resolver.caltech.edu/CaltechAUTHORS:20160930-133917913

Frank, Rupert L. and Lenzmann, Enno and Silvestre, Luis (2016) Uniqueness of Radial Solutions for the Fractional Laplacian. Communications on Pure and Applied Mathematics, 69 (9). pp. 1671-1726. ISSN 0010-3640. http://resolver.caltech.edu/CaltechAUTHORS:20160811-074144777

Frank, Rupert L. and Killip, Rowan and Nam, Phan Thành (2016) Nonexistence of Large Nuclei in the Liquid Drop Model. Letters in Mathematical Physics, 106 (8). pp. 1033-1036. ISSN 0377-9017 . http://resolver.caltech.edu/CaltechAUTHORS:20160805-093315174

Frank, Rupert L. and Lieb, Elliott H. (2016) A 'liquid-solid' phase transition in a simple model for swarming, based on the 'no flat-spots' theorem for subharmonic functions. . (Submitted) http://resolver.caltech.edu/CaltechAUTHORS:20170428-161302774

Frank, Rupert L. and Hainzl, Christian and Schlein, Benjamin et al. (2016) Incompatibility of Time-Dependent Bogoliubov–de-Gennes and Ginzburg–Landau Equations. Letters in Mathematical Physics, 106 (7). pp. 913-923. ISSN 0377-9017 . http://resolver.caltech.edu/CaltechAUTHORS:20160722-140945826

Frank, Rupert L. and Lieb, Elliott H. and Sabin, Julien (2016) Maximizers for the Stein–Tomas Inequality. Geometric and Functional Analysis, 26 (4). pp. 1095-1134. ISSN 1016-443X . http://resolver.caltech.edu/CaltechAUTHORS:20161129-084514277

Frank, Rupert L. and Geisinger, Leander (2016) Refined semiclassical asymptotics for fractional powers of the Laplace operator. Journal für die reine und angewandte Mathematik, 2016 (712). pp. 1-37. ISSN 0075-4102. http://resolver.caltech.edu/CaltechAUTHORS:20160317-104639269

Carlen, Eric A. and Frank, Rupert L. and Lieb, Elliott H. (2016) Some operator and trace function convexity theorems. Linear Algebra and its Applications, 490 . pp. 174-185. ISSN 0024-3795. http://resolver.caltech.edu/CaltechAUTHORS:20160225-075610491

Frank, Rupert L. and Hainzl, Christian and Seiringer, Robert et al. (2016) The External Field Dependence of the BCS Critical Temperature. Communications in Mathematical Physics, 342 (1). pp. 189-216. ISSN 0010-3616. http://resolver.caltech.edu/CaltechAUTHORS:20160303-112827308

Frank, Rupert L. and Sabin, Julien (2016) The Stein-Tomas inequality in trace ideals. Séminaire Laurent Schwartz - EDP et applications, 15 . Art. No. 12. http://resolver.caltech.edu/CaltechAUTHORS:20170428-154841451

2015

Frank, Rupert L. and Lieb, Elliott H. (2015) A Compactness Lemma and Its Application to the Existence of Minimizers for the Liquid Drop Model. SIAM Journal on Mathematical Analysis, 47 (6). pp. 4436-4450. ISSN 0036-1410. http://resolver.caltech.edu/CaltechAUTHORS:20160115-123530660

Frank, R. L. and Hainzi, C. and Seiringer, R. et al. (2015) Microscopic Derivation of the Ginzburg-Landau Model. . (Submitted) http://resolver.caltech.edu/CaltechAUTHORS:20170505-112911639

Frank, Rupert L. and Geisinger, Leander (2015) The Ground State Energy of a Polaron in a Strong Magnetic Field. Communications in Mathematical Physics, 338 (1). pp. 1-29. ISSN 0010-3616. http://resolver.caltech.edu/CaltechAUTHORS:20150706-132935949

Ekholm, Tomas and Frank, Rupert L. and Kovařík, Hynek (2015) Weak perturbations of the p-Laplacian. Calculus of Variations and Partial Differential Equations, 53 (3-4). pp. 781-801. ISSN 0944-2669. http://resolver.caltech.edu/CaltechAUTHORS:20150604-085020731

Frank, Rupert L. and Pushnitski, Alexander (2015) The spectral density of a product of spectral projections. Journal of Functional Analysis, 268 (12). pp. 3867-3894. ISSN 0022-1236. http://resolver.caltech.edu/CaltechAUTHORS:20150612-085811844

Frank, Rupert L. and Pushnitski, Alexander (2015) Trace Class Conditions for Functions of Schrödinger Operators. Communications in Mathematical Physics, 335 (1). pp. 477-496. ISSN 0010-3616. http://resolver.caltech.edu/CaltechAUTHORS:20150330-070612488

Frank, Rupert L. and Lenzmann, Enno (2015) Uniqueness and Nondegeneracy of Ground States for (−Δ)^sQ+Q−Q^(α+1)=0 in R. . (Submitted) http://resolver.caltech.edu/CaltechAUTHORS:20170501-072727175

Bengurla, Rafael D. and Frank, Rupert L. and Lieb, Elliott H. (2015) Ground state energy of large polaron systems. Journal of Mathematical Physics, 56 (2). Art. No. 021901. ISSN 0022-2488. http://resolver.caltech.edu/CaltechAUTHORS:20150409-135549549

Frank, Rupert L. and González, María del Mar and Monticelli, Dario D. et al. (2015) An extension problem for the CR fractional Laplacian. Advances in Mathematics, 270 . pp. 97-137. ISSN 0001-8708. http://resolver.caltech.edu/CaltechAUTHORS:20150226-131020302

2014

Bellazzini, Jacopo and Frank, Rupert L. and Visciglia, Nicola (2014) Maximizers for Gagliardo–Nirenberg inequalities and related non-local problems. Mathematische Annalen, 360 (3-4). pp. 653-673. ISSN 0025-5831. http://resolver.caltech.edu/CaltechAUTHORS:20141211-085533969

Frank, Rupert L. and Schlein, Benjamin (2014) Dynamics of a Strongly Coupled Polaron. Letters in Mathematical Physics, 104 (8). pp. 911-929. ISSN 0377-9017 . http://resolver.caltech.edu/CaltechAUTHORS:20140708-142118299

Frank, Rupert L. and Lewin, Mathieu and Lieb, Elliott H. et al. (2014) Strichartz inequality for orthonormal functions. Journal of the European Mathematical Society, 16 (7). pp. 1507-1526. ISSN 1435-9855. http://resolver.caltech.edu/CaltechAUTHORS:20141023-082135692

Frank, Rupert L. and Lenz, Daniel and Wingert, Daniel (2014) Intrinsic metrics for non-local symmetric Dirichlet forms and applications to spectral theory. Journal of Functional Analysis, 266 (8). pp. 4765-4808. ISSN 0022-1236. http://resolver.caltech.edu/CaltechAUTHORS:20170501-080259012

Bellazzini, Jacopo and Frank, Rupert L. and Lieb, Elliott H. et al. (2014) Existence of ground states for negative ions at the binding threshold. Reviews in Mathematical Physics, 26 (01). Art. No. 1350021. ISSN 0129-055X. http://resolver.caltech.edu/CaltechAUTHORS:20170504-103757590

Carlen, Eric A. and Frank, Rupert L. and Lieb, Elliott H. (2014) Stability Estimates for the Lowest Eigenvalue of a Schrödinger Operator. Geometric and Functional Analysis, 24 (1). pp. 63-84. ISSN 1016-443X . http://resolver.caltech.edu/CaltechAUTHORS:20140422-141713585

Frank, Rupert L. (2014) Cwikel’s theorem and the CLR inequality. Journal of Spectral Theory, 4 (1). pp. 1-21. ISSN 1664-039X. http://resolver.caltech.edu/CaltechAUTHORS:20140530-072438434

2013

Frank, Rupert L. and Lieb, Elliott H. (2013) Monotonicity of a relative Rényi entropy. Journal of Mathematical Physics, 54 (12). Art. No. 122201. ISSN 0022-2488. http://resolver.caltech.edu/CaltechAUTHORS:20140130-111730599

Frank, Rupert L. and Lieb, Elliott H. (2013) Extended Quantum Conditional Entropy and Quantum Uncertainty Inequalities. Communications in Mathematical Physics, 323 (2). pp. 487-495. ISSN 0010-3616. http://resolver.caltech.edu/CaltechAUTHORS:20170501-112412599

Frank, Rupert L. and Lenzmann, Enno (2013) Uniqueness of non-linear ground states for fractional Laplacians in R. Acta Mathematica, 210 (2). pp. 261-318. ISSN 0001-5962. http://resolver.caltech.edu/CaltechAUTHORS:20130807-152723442

Frank, Rupert L. and Kovařík, Hynek (2013) Heat kernels of metric trees and applications. SIAM Journal on Mathematical Analysis, 45 (3). pp. 1027-1046. ISSN 0036-1410. http://resolver.caltech.edu/CaltechAUTHORS:20130815-102433930

Frank, Rupert L. and Lieb, Elliott H. and Seiringer, Robert (2013) Symmetry of Bipolaron Bound States for Small Coulomb Repulsion. Communications in Mathematical Physics, 319 (2). pp. 557-573. ISSN 0010-3616. http://resolver.caltech.edu/CaltechAUTHORS:20170502-144700862

Frank, Rupert L. and Lewin, Mathieu and Lieb, Elliott H. et al. (2013) A positive density analogue of the Lieb–Thirring inequality. Duke Mathematical Journal, 162 (3). pp. 435-495. ISSN 0012-7094. http://resolver.caltech.edu/CaltechAUTHORS:20130319-101032718

Frank, Rupert L. and Hainzl, Christian and Seiringer, Robert et al. (2013) Derivation of Ginzburg-Landau theory for a one-dimensional system with contact interaction. In: Operator Methods in Mathematical Physics. Operator Theory: Advances and Applications. No.227. Springer , Basel, pp. 57-88. ISBN 978-3-0348-0531-5. http://resolver.caltech.edu/CaltechAUTHORS:20170501-083839909

2012

Frank, Rupert L. and Lieb, Elliott H. (2012) Entropy and the Uncertainty Principle. Annales Henri Poincaré, 13 (8). pp. 1711-1717. ISSN 1424-0637. http://resolver.caltech.edu/CaltechAUTHORS:20170501-103316603

Frank, Rupert L. and Geisinger, Leander (2012) Semi-classical analysis of the Laplace operator with Robin boundary conditions. Bulletin of Mathematical Sciences, 2 (2). pp. 281-319. ISSN 1664-3615. http://resolver.caltech.edu/CaltechAUTHORS:20170505-092151992

Frank, Rupert L. and Lieb, Elliott H. and Seiringer, Robert et al. (2012) Ground state properties of multi-polaron systems. . (Submitted) http://resolver.caltech.edu/CaltechAUTHORS:20170505-111204119

Frank, Rupert L. and Seiringer, Robert (2012) Lieb-Thirring inequality for a model of particles with point interactions. Journal of Mathematical Physics, 53 (9). Art. No. 095201. ISSN 0022-2488. http://resolver.caltech.edu/CaltechAUTHORS:20170501-113527750

Frank, Rupert L. and Hainzl, Christian and Seiringer, Robert et al. (2012) Microscopic Derivation of Ginzburg-Landau Theory. Journal of the American Mathematical Society, 25 (3). pp. 667-713. ISSN 0894-0347. http://resolver.caltech.edu/CaltechAUTHORS:20170501-090207067

Chen, Shibing and Frank, Rupert L. and Weth, Tobias (2012) Remainder terms in the fractional Sobolev inequality. . (Submitted) http://resolver.caltech.edu/CaltechAUTHORS:20170502-150250004

Frank, Rupert L. and Loss, Michael (2012) Hardy-Sobolev-Maz'ya inequalities for arbitrary domains. Journal de Mathématiques Pures et Appliquées, 97 (1). pp. 39-54. ISSN 0021-7824. http://resolver.caltech.edu/CaltechAUTHORS:20170501-085309159

Frank, Rupert L. and Lieb, Elliott H. (2012) Sharp constants in several inequalities on the Heisenberg group. Annals of Mathematics, 176 (1). pp. 349-381. ISSN 0003-486X. http://resolver.caltech.edu/CaltechAUTHORS:20170501-064349426

Frank, Rupert L. and Lieb, Elliott H. (2012) A new, rearrangement-free proof of the sharp Hardy-Littlewood-Sobolev inequality. In: Spectral Theory, Function Spaces and Inequalities. Operator Theory: Advances and Applications. No.219. Springer , Basel, pp. 55-67. ISBN 978-3-0348-0263-5. http://resolver.caltech.edu/CaltechAUTHORS:20170501-075729792

2011

Dyda, Bartlomiej and Frank, Rupert L. (2011) Fractional Hardy-Sobolev-Maz'ya inequality for domains. . (Submitted) http://resolver.caltech.edu/CaltechAUTHORS:20170501-094456500

Frank, Rupert L. and Olofsson, Rikard (2011) Eigenvalue bounds for Schrödinger operators with a homogeneous magnetic field. Letters in Mathematical Physics, 97 . pp. 227-241. ISSN 0377-9017 . http://resolver.caltech.edu/CaltechAUTHORS:20170501-072120225

Cornean, Horia D. and Fournais, Søren and Frank, Rupert L. et al. (2011) Sharp trace asymptotics for a class of 2D-magnetic operators. . (Submitted) http://resolver.caltech.edu/CaltechAUTHORS:20170501-100604320

Frank, Rupert L. (2011) Eigenvalue bounds for Schrödinger operators with complex potentials. Bulletin of the London Mathematical Society, 43 (4). pp. 745-750. ISSN 0024-6093. http://resolver.caltech.edu/CaltechAUTHORS:20170501-065723391

Frank, Rupert L. and Lieb, Elliott H. and Seiringer, Robert (2011) Binding of Polarons and Atoms at Threshold. . (Submitted) http://resolver.caltech.edu/CaltechAUTHORS:20170501-091837793

Frank, Rupert L. and Lieb, Elliott H. and Seiringer, Robert et al. (2011) Stability and Absence of Binding for Multi-Polaron Systems. Publications mathématiques de l'IHÉS, 113 (1). pp. 39-67. ISSN 0073-8301. http://resolver.caltech.edu/CaltechAUTHORS:20170501-071121790

Frank, Rupert L. and Lieb, Elliott H. (2011) Possible Lattice Distortions in the Hubbard Model for Graphene. . (Submitted) http://resolver.caltech.edu/CaltechAUTHORS:20170501-082647988

Frank, Rupert L. and Simon, Barry (2011) Critical Lieb-Thirring bounds in gaps and the generalized Nevai conjecture for finite gap Jacobi matrices. Duke Mathematical Journal, 157 (3). pp. 461-493. ISSN 0012-7094. http://resolver.caltech.edu/CaltechAUTHORS:20110502-112300651

Frank, Rupert L. and Lewin, Mathieu and Lieb, Elliott H. et al. (2011) Energy Cost to Make a Hole in the Fermi Sea. Physical Review Letters, 106 (15). Art. No. 150402. ISSN 0031-9007. http://resolver.caltech.edu/CaltechAUTHORS:20170501-093433748

Ekholm, Tomas and Frank, Rupert L. and Kovařík, Hynek (2011) Eigenvalue estimates for Schrödinger operators on metric trees. Advances in Mathematics, 226 (6). pp. 5165-5197. ISSN 0001-8708. http://resolver.caltech.edu/CaltechAUTHORS:20170512-094610802

Frank, Rupert L. and Laptev, Ari and Seiringer, Robert (2011) A sharp bound on eigenvalues of Schröedinger operators on the half-line with complex-valued potentials. In: Spectral Theory and Analysis. Operator Theory: Advances and Applications. No.214. Springer , Basel, pp. 39-44. ISBN 9783764399948. http://resolver.caltech.edu/CaltechAUTHORS:20170526-100635987

Frank, Rupert L. and Morozov, Sergey and Vugalter, Semjon (2011) Weakly coupled bound states of Pauli operators. Calculus of Variations and Partial Differential Equations, 40 (1). pp. 253-271. ISSN 0944-2669. http://resolver.caltech.edu/CaltechAUTHORS:20170526-094859466

Frank, Rupert L. and Lieb, Elliott H. and Seiringer, Robert et al. (2011) Binding, Stability, and Non-binding of Multi-polaron Systems. In: Mathematical Results in Quantum Physics. World Scientific , Singapore, pp. 21-32. ISBN 9789814350365. http://resolver.caltech.edu/CaltechAUTHORS:20170501-075001254

Frank, Rupert L. (2011) On the uniqueness of ground states of non-local equations. Journées équations aux dérivées partielles, 2011 . A5. ISSN 0752-0360. http://resolver.caltech.edu/CaltechAUTHORS:20170501-111716146

Frank, Rupert L. and Lieb, Elliott H. (2011) Spherical reflection positivity and the Hardy-Littlewood-Sobolev inequality. In: Concentration, Functional Inequalities and Isoperimetry. Contemporary Mathematics. No.545. American Mathematical Society , Providence, RI, pp. 89-102. ISBN 978-0-8218-4971-2. http://resolver.caltech.edu/CaltechAUTHORS:20170501-070506766

Frank, Rupert L. and Geisinger, Leander (2011) Two-term spectral asymptotics for the Dirichlet Laplacian on a bounded domain. In: Mathematical Results in Quantum Physics. World Scientific , Singapore, pp. 138-147. ISBN 9789814350365. http://resolver.caltech.edu/CaltechAUTHORS:20170501-080935483

2010

Frank, Rupert L. and Lenzmann, Enno (2010) On ground states for the L^2-critical boson star equation. . (Submitted) http://resolver.caltech.edu/CaltechAUTHORS:20170526-101905288

Frank, Rupert L. and Lieb, Elliott H. (2010) Inversion positivity and the sharp Hardy–Littlewood–Sobolev inequality. Calculus of Variations and Partial Differential Equations, 39 (1-2). pp. 85-99. ISSN 0944-2669. http://resolver.caltech.edu/CaltechAUTHORS:20170510-143424777

Frank, Rupert L. and Lieb, Elliott H. and Seiringer, Robert et al. (2010) Bipolaron and N-Polaron Binding Energies. Physical Review Letters, 104 (21). Art. No. 210402. ISSN 0031-9007. http://resolver.caltech.edu/CaltechAUTHORS:20170501-064924933

Frank, Rupert L. and Lieb, Elliott H. and Seiringer, Robert (2010) Equivalence of Sobolev inequalities and Lieb-Thirring inequalities. In: XVIth International Congress on Mathematical Physics. World Scientific , Singapore, pp. 523-535. ISBN 978-981-4304-62-7 . http://resolver.caltech.edu/CaltechAUTHORS:20170526-125941569

Frank, Rupert L. and Laptev, Ari (2010) Inequalities between Dirichlet and Neumann eigenvalues on the Heisenberg group. International Mathematics Research Notices, 2010 (15). pp. 2889-2902. ISSN 1073-7928. http://resolver.caltech.edu/CaltechAUTHORS:20170526-092032067

Frank, Rupert L. and Seiringer, Robert (2010) Sharp Fractional Hardy Inequalities in Half-Spaces. In: Around the Research of Vladimir Maz'ya I. International Mathematical Series. No.11. Springer New York , pp. 161-167. ISBN 978-1-4419-1340-1. http://resolver.caltech.edu/CaltechAUTHORS:20170526-131557265

2009

Frank, Rupert L. and Lieb, Elliott H. and Seiringer, Robert et al. (2009) Müeller's Exchange-Correlation Energy in Density-Matrix-Functional Theory. . (Submitted) http://resolver.caltech.edu/CaltechAUTHORS:20170510-091442211

Frank, Rupert L. (2009) A Simple Proof of Hardy-Lieb-Thirring Inequalities. Communications in Mathematical Physics, 290 (2). pp. 789-800. ISSN 0010-3616. http://resolver.caltech.edu/CaltechAUTHORS:20170512-093621400

Breuer, Jonathan and Frank, Rupert L. (2009) Singular spectrum for radial trees. Reviews in Mathematical Physics, 21 (7). pp. 929-945. ISSN 0129-055X. http://resolver.caltech.edu/CaltechAUTHORS:20091012-105116089

Frank, Rupert L. (2009) A note on low energy scattering for homogeneous long range potentials. Annales Henri Poincaré, 10 (3). pp. 573-575. ISSN 1424-0637. http://resolver.caltech.edu/CaltechAUTHORS:20170526-100006703

Frank, Rupert L. and Lenzmann, Enno (2009) Uniqueness of ground states for the L^2-critical boson star equation. . (Submitted) http://resolver.caltech.edu/CaltechAUTHORS:20170526-093631237

Frank, Rupert L. (2009) Remarks on eigenvalue estimates and semigroup domination. . (Submitted) http://resolver.caltech.edu/CaltechAUTHORS:20170526-092635990

2008

Frank, Rupert L. and Seiringer, Robert (2008) Non-linear ground state representations and sharp Hardy inequalities. Journal of Functional Analysis, 255 (12). pp. 3407-3430. ISSN 0022-1236. http://resolver.caltech.edu/CaltechAUTHORS:20170510-155935658

Frank, Rupert L. and Simon, Barry and Weidl, Timo (2008) Eigenvalue Bounds for Perturbations of Schrödinger Operators and Jacobi Matrices With Regular Ground States. Communications in Mathematical Physics, 282 (1). pp. 199-208. ISSN 0010-3616. http://resolver.caltech.edu/CaltechAUTHORS:20170408-144423477

Frank, Rupert L. and Siedentop, Heinz and Warzel, Simone (2008) The Energy of Heavy Atoms According to Brown and Ravenhall: The Scott Correction. . (Submitted) http://resolver.caltech.edu/CaltechAUTHORS:20170512-100456574

Frank, Rupert L. and Siedentop, Heinz and Warzel, Simone (2008) The Ground State Energy of Heavy Atoms: Relativistic Lowering of the Leading Energy Correction. Communications in Mathematical Physics, 278 (2). pp. 549-566. ISSN 0010-3616. http://resolver.caltech.edu/CaltechAUTHORS:20170510-160420593

Ekholm, Tomas and Frank, Rupert (2008) Lieb–Thirring inequalities on the half-line with critical exponent. European Mathematical Society, 10 (3). pp. 739-755. ISSN 1435-9855. http://resolver.caltech.edu/CaltechAUTHORS:20170531-151816388

2007

Frank, Rupert L. and Laptev, Ari and Molchanov, Stanislav (2007) Eigenvalue estimates for magnetic Schrödinger operators in domains. Proceedings of the American Mathematical Society, 136 (12). pp. 4245-4255. ISSN 0002-9939. http://resolver.caltech.edu/CaltechAUTHORS:20170511-070749185

Frank, Rupert L. and Lieb, Elliott H. and Seiringer, Robert (2007) Number of Bound States of Schröedinger Operators with Matrix-Valued Potentials. Letters in Mathematical Physics, 82 (2-3). pp. 107-116. ISSN 0377-9017 . http://resolver.caltech.edu/CaltechAUTHORS:20170510-095237526

Frank, Rupert L. and Hainzl, Christian and Naboko, Serguei et al. (2007) The critical temperature for the BCS equation at weak coupling. Journal of Geometric Analysis, 17 (4). pp. 559-567. ISSN 1050-6926. http://resolver.caltech.edu/CaltechAUTHORS:20170510-105303048

Frank, Rupert L. and Laptev, Ari (2007) Spectral inequalities for Schrödinger operators with surface potentials. . (Submitted) http://resolver.caltech.edu/CaltechAUTHORS:20170512-095723566

Ekholm, Tomas and Frank, Rupert L. and Kovařík, Hynek (2007) Remarks about Hardy inequalities on metric trees. . (Submitted) http://resolver.caltech.edu/CaltechAUTHORS:20170512-090412324

Frank, Rupert L. and Lieb, Elliott H. and Seiringer, Robert (2007) Hardy-Lieb-Thirring inequalities for fractional Schrödinger operators. Journal of the American Mathematical Society, 21 (4). pp. 925-950. ISSN 0894-0347. http://resolver.caltech.edu/CaltechAUTHORS:20170526-134159102

Frank, Rupert L. and Hansson, Anders (2007) Eigenvalue estimates for the Aharonov-Bohm operator in a domain. . http://resolver.caltech.edu/CaltechAUTHORS:20170510-090747676

Frank, Rupert L. and Loss, Michael and Weidl, Timo (2007) Pόlya's conjecture in the presence of a constant magnetic field. . (Submitted) http://resolver.caltech.edu/CaltechAUTHORS:20170510-073002205

Frank, Rupert L. and Lieb, Elliott H. and Seiringer, Robert (2007) Stability of Relativistic Matter with Magnetic Fields for Nuclear Charges up to the Critical Value. Communications in Mathematical Physics, 275 (2). pp. 479-489. ISSN 0010-3616. http://resolver.caltech.edu/CaltechAUTHORS:20170601-073744902

Frank, Rupert L. (2007) On the asymptotic number of edge states for magnetic Schrödinger operators. Proceedings of the London Mathematical Society, 95 (1). pp. 1-19. ISSN 0024-6115. http://resolver.caltech.edu/CaltechAUTHORS:20170601-081138045

Benguria, Rafael D. and Frank, Rupert L. and Loss, Michael (2007) The sharp constant in the Hardy-Sobolev-Maz’ya inequality in the three dimensional upper half-space. . (Submitted) http://resolver.caltech.edu/CaltechAUTHORS:20170511-064913855

Exner, Pavel and Frank, Rupert L. (2007) Absolute Continuity of the Spectrum for Periodically Modulated Leaky Wires in R^3. Annales Henri Poincaré, 8 (2). pp. 241-263. ISSN 1424-0637. http://resolver.caltech.edu/CaltechAUTHORS:20170601-083108196

2006

Frank, Rupert L. and Laptev, Ari and Lieb, Elliott H. et al. (2006) Lieb–Thirring Inequalities for Schrödinger Operators with Complex-valued Potentials. Letters in Mathematical Physics, 77 (3). pp. 309-316. ISSN 0377-9017 . http://resolver.caltech.edu/CaltechAUTHORS:20170601-075251570

This list was generated on Tue Jul 16 22:15:38 2019 PDT.