Inequalities: Selecta of Elliott H. Lieb

Front Matter....Pages I-IX
Commentaries....Pages 1-29
Front Matter....Pages 31-31
Theory of Ferromagnetism and the Ordering of Electronic Energy Levels....Pages 33-41
Ordering Energy Levels of Interacting Spin Systems....Pages 43-45
Entropy Inequalities....Pages 47-57
A Fundamental Property of Quantum-Mechanical Entropy....Pages 59-61
Proof of the strong subadditivity of quantum-mechanical entropy....Pages 63-66
Some Convexity and Subadditivity Properties of Entropy....Pages 67-79
A Refinement of Simon’s Correlation Inequality....Pages 81-89
Two Theorems on the Hubbard Model....Pages 91-94
Magnetic Properties of Some Itinerant-Electron Systems at T > 0....Pages 95-98
Front Matter....Pages 99-99
Proofs of some Conjectures on Permanents....Pages 101-108
Concavity Properties and a Generating Function for Stirling Numbers....Pages 109-112
Convex Trace Functions and the Wigner-Yanase-Dyson Conjecture....Pages 113-134
Some Operator Inequalities of the Schwarz Type....Pages 135-139
Inequalities for Some Operator and Matrix Functions....Pages 141-145
Positive Linear Maps which are Order Bounded on C* Subalgebras....Pages 147-149
Optimal Hypercontractivity for Fermi Fields and Related Non-Commutative Integration Inequalities....Pages 151-170
Sharp uniform convexity and smoothness inequalities for trace norms....Pages 171-190
A Minkowski Type Trace Inequality and Strong Subadditivity of Quantum Entropy....Pages 191-200
Front Matter....Pages 201-201
Inequalities for the Moments of the Eigenvalues of the Schrödinger Hamiltonian and their Relation to Sobolev Inequalities....Pages 203-237
Front Matter....Pages 201-201
On Semi-Classical Bounds for Eigenvalues of Schrödinger Operators....Pages 239-241
The Number of Bound States of One-Body Schroedinger Operators and the Weyl Problem....Pages 243-254
Improved Lower Bound on the Indirect Coulomb Energy....Pages 255-267
Density Functionals for Coulomb Systems....Pages 269-303
On Characteristic Exponents in Turbulence....Pages 305-312
Baryon Mass Inequalities in Quark Models....Pages 313-316
Kinetic Energy Bounds and their Application to the Stability of Matter....Pages 317-328
A sharp bound for an eigenvalue moment of the one-dimensional Schrödinger operator....Pages 329-341
Front Matter....Pages 343-343
The Classical Limit of Quantum Spin Systems....Pages 345-358
Proof of an Entropy Conjecture of Wehrl....Pages 359-365
Quantum Coherent Operators: A Generalization of Coherent States....Pages 367-376
Coherent States as a Tool for Obtaining Rigorous Bounds....Pages 377-388
Front Matter....Pages 389-389
A General Rearrangement Inequality for Multiple Integrals....Pages 391-401
Some inequalities for Gaussian measures and the long-range order of the one-dimensional plasma....Pages 403-416
Best Constants in Young’s Inequality, Its Converse, and Its Generalization to More than Three Functions....Pages 417-439
On Extensions of the Brunn-Minkowski and Prékopa-Leindler Theorems, Including Inequalities for Log Concave Functions, and with an Application to the Diffusion Equation....Pages 441-464
Existence and Uniqueness of the Minimizing Solution of Choquard’s Nonlinear Equation....Pages 465-467
Symmetric Decreasing Rearrangement Can Be Discontinuous....Pages 479-482
The (NON) Continuity of Symmetric Decreasing Rearrangement....Pages 483-496
On the Case of Equality in the Brunn-Minkowski Inequality for Capacity....Pages 497-511
Front Matter....Pages 513-513
An L p Bound for the Riesz and Bessel Potentials of Orthonormal Functions....Pages 515-521
A Relation Between Pointwise Convergence of Functions and Convergence of Functionals....Pages 523-527
Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities....Pages 529-554
On the lowest eigenvalue of the Laplacian for the intersection of two domains....Pages 555-562
Minimum Action Solutions of Some Vector Field Equations....Pages 563-579
Sobolev Inequalities with Remainder Terms....Pages 581-594
Gaussian kernels have only Gaussian maximizers*....Pages 595-624
Integral bounds for radar ambiguity functions and Wigner distributions....Pages 625-630
Front Matter....Pages 631-631
Calcul Des Variations. — Estimations d’énergie pour des applications de R 3 à....Pages 633-636
Singularities Of Energy-Minimizing Maps From The Ball To The Sphere....Pages 637-639
Co-Area, Liquid Crystals, and Minimal Surfaces....Pages 641-662
Counting Singularities in Liquid Crystals....Pages 663-678
Symmetry of the Ginzburg Landau Minimizer in a Disc....Pages 679-693
Back Matter....Pages 695-711