Inequalities: Selecta of Elliott H. Lieb

Front Cover......Page 1
Half Title......Page 2
Elliott H. Lieb......Page 3
Title Page......Page 4
Copyright......Page 5
Preface......Page 6
Contents......Page 8
Commentaries......Page 12
Part I. Inequalities Related to Statistical Mechanics and Condensed Matter......Page 42
Theory of Ferromagnetism and the Ordering of Electronic Energy Levels (with D.C. Mattis)......Page 44
Ordering Energy Levels of Interacting Spin Systems (with D.C. Mattis)......Page 54
Entropy Inequalities (with H. Araki)......Page 58
A Fundamental Property of Quantum-Mechanical Entropy (with M.B. Ruskai)......Page 70
Proof of the Strong Subadditivity of Quantum-Mechanical Entropy (with M.B. Ruskai)......Page 74
Some Convexity and Subadditivity Properties of Entropy......Page 78
A Refinement of Simon's Correlation Inequality......Page 92
Two Theorems on the Hubbard Model......Page 102
Magnetic Properties of Some Itinerant-Electron Systems at T > 0 (with M. Aizenman)......Page 106
Part II. Matrix Inequalities and Combinatorics Proofs of Some Conjectures on Permanents......Page 110
Concavity Properties and a Generating Function for Stirling Numbers......Page 120
Convex Trace Functions and the Wigner-Yanase-Dyson Conjecture......Page 124
Some Operator Inequalities of the Schwarz Type (with M.B. Ruskai)......Page 146
Inequalities for Some Operator and Matrix Functions......Page 152
Positive Linear Maps Which Are Order Bounded on C` Subalgebras (with M. Aizenman and E.B. Davies)......Page 158
Optimal Hypercontractivity for Fermi Fields and Related Non-Commutative Integration Inequalities (with E. Carlen)......Page 162
Sharp Uniform Convexity and Smoothness Inequalities for Trace Norms (with K. Ball and E. Carlen)......Page 182
A Minkowski Type Trace Inequality and Strong Subadditivity of Quantum Entropy (with E. Carlen)......Page 202
Part III. Inequalities Related to the Stability of Matter......Page 212
III.1 Inequalities for the Moments of the Eigenvalues of the Schrodinger Hamiltonian and Their Relation to Sobolev Inequalities (with W. Thirring)......Page 214
III.2 On Semi-Classical Bounds for Eigenvalues of Schrodinger Operators (with M. Aizenman)......Page 250
III.3 The Number of Bound States of One-Body Schrodinger Operators and the Weyl Problem......Page 254
III.4 Improved Lower Bound on the Indirect Coulomb Energy (with S. Oxford)......Page 266
III.5 Density Functionals for Coulomb Systems......Page 280
III.6 On Characteristic Exponents in Turbulence......Page 316
III.7 Baryon Mass Inequalities in Quark Models......Page 324
III.8 Kinetic Energy Bounds and Their Application to the Stability of Matter......Page 328
III.9 A Sharp Bound for an Eigenvalue Moment of the One-Dimensional Schrodinger Operator (with D. Hundertmark and L.E. Thomas)......Page 340
Part IV. Coherent States......Page 354
IV.1 The Classical Limit of Quantum Spin Systems......Page 356
IV.2 Proof of an Entropy Conjecture of Wehrl......Page 370
IV.3 Quantum Coherent Operators: A Generalization of Coherent States (with J.P. Solovej)......Page 378
IV.4 Coherent States as a Tool for Obtaining Rigorous Bounds......Page 388
Part V. Brunn-Minkowski Inequality and Rearrangements......Page 400
V.1 A General Rearrangement Inequality for Multiple Integrals (with H.J. Brascamp and J.M. Luttinger)......Page 402
V.2 Some Inequalities for Gaussian Measures and the Long-Range Order of the One-Dimensional Plasma (with H.J. Brascamp)......Page 414
V.3 Best Constants in Young's Inequality, Its Converse and Its Generalization to More than Three Functions (with H.J. Brascamp)......Page 428
V.4 On Extensions of the Brunn-Minkowski and Prekopa-Leindler Theorems, Including Inequalities for Log Concave Functions and with an Application to the Diffusion Equation (with H.J. Brascamp)......Page 452
V.5 Existence and Uniqueness of the Minimizing Solution of Choquard's Nonlinear Equation......Page 476
V.6 Symmetric Decreasing Rearrangement Can Be Discontinuous (with F. Almgren)......Page 490
V.7 The (Non) Continuity of Symmetric Decreasing Rearrangement (with F. Almgren)......Page 494
V.8 On the Case of Equality in the Brunn-Minkowski Inequality for Capacity (with L. Cafarelli and D. Jerison)......Page 508
Part VI. General Analysis......Page 524
VI.1 An U' Bound for the Riesz and Bessel Potentials of Orthonormal Functions......Page 526
VI.2 A Relation Between Pointwise Convergence of Functions and Convergence of Functionals (with H. Brezis)......Page 534
VI.3 Sharp Constants in the Hardy-Littlewood-Sobolev and Related Inequalities......Page 540
VI.4 On the Lowest Eigenvalue of the Laplacian for the Intersection of Two Domains......Page 566
VI.5 Minimum Action Solutions of Some Vector Field Equations (with H. Brezis)......Page 574
VI.6 Sobolev Inequalities with Remainder Terms (with H. Brezis)......Page 592
VI.7 Gaussian Kernels Have Only Gaussian Maximizers......Page 606
VI.8 Integral Bounds for Radar Ambiguity Functions and Wigner Distributions......Page 636
Part VII. Inequalities Related to Harmonic Maps......Page 642
VII.1 Estimations d'energie pour des applications de R3 a valeurs dans S2 (with H. Brezis and J-M. Coron)......Page 644
VII.2 Singularities of Energy Minimizing Maps from the Ball to the Sphere (with F. Almgren)......Page 648
VII.3 Co-area, Liquid Crystals, and Minimal Surfaces (with F. Almgren and W. Browder)......Page 652
VII.4 Counting Singularities in Liquid Crystals (with F. Almgren)......Page 674
VII.5 Symmetry of the Ginzburg-Landau Minimizer in a Disc (with M. Loss)......Page 690
Publications of Elliott H. Lieb......Page 706