Title | Inequalities [electronic resource] : Selecta of Elliott H. Lieb / edited by Michael Loss, Mary Beth Ruskai |
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Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2002 |
Connect to | http://dx.doi.org/10.1007/978-3-642-55925-9 |
Descript | IX, 711 p. online resource |
Commentaries -- I. Inequalities Related to Statistical Mechanics and Condensed Matter -- I.1 Theory of Ferromagnetism and the Ordering of Electronic Energy Levels -- I.2 Ordering Energy Levels of Interacting Spin Systems -- I.3 Entropy Inequalities (with H. Araki) -- I.4 A Fundamental Property of Quantum-Mechanical Entropy -- I.5 Proof of the Strong Subadditivity of Quantum-Mechanical Entropy -- I.6 Some Convexity and Subadditivity Properties of Entropy -- I.7 A Refinement of Simonโs Correlation Inequality -- I.8 Two Theorems on the Hubbard Model -- I.9 Magnetic Properties of Some Itinerant-Electron Systems at T > 0 -- II. Matrix Inequalities and Combinatorics -- II.1 Proofs of Some Conjectures on Permanents -- II.2 Concavity Properties and a Generating Function for Stirling Numbers -- II.3 Convex Trace Functions and the Wigner-Yanase-Dyson Conjecture -- II.4 Some Operator Inequalities of the Schwarz Type -- II.5 Inequalities for Some Operator and Matrix Functions -- II.6 Positive Linear Maps Which Are Order Bounded on C* Subalgebras -- II. 7 Optimal Hypercontractivity for Fermi Fields and Related Non-Commutative Integration Inequalities -- II. 8 Sharp Uniform Convexity and Smoothness Inequalities for Trace Norms -- II.9 A Minkowski Type Trace Inequality and Strong Subadditivity of Quantum Entropy -- III. Inequalities Related to the Stability of Matter -- III.1 Inequalities for the Moments of the Eigenvalues of the Schrรถdinger Hamiltonian and Their Relation to Sobolev Inequalities -- III.2 On Semi-Classical Bounds for Eigenvalues of Schrรถdinger Operators -- III.3 The Number of Bound States of One-Body Schrรถdinger Operators and the Weyl Problem -- III.4 Improved Lower Bound on the Indirect Coulomb Energy -- III.5 Density Functionals for Coulomb Systems -- III.6 On Characteristic Exponents in Turbulence -- III.7 Baryon Mass Inequalities in Quark Models -- III.8 Kinetic Energy Bounds and Their Application to the Stability of Matter -- III.9 A Sharp Bound for an Eigenvalue Moment of the One-Dimensional Schrรถdinger Operator -- IV. Coherent States -- IV.1 The Classical Limit of Quantum Spin Systems -- IV.2 Proof of an Entropy Conjecture of Wehrl -- IV.3 Quantum Coherent Operators: A Generalization of Coherent States -- IV.4 Coherent States as a Tool for Obtaining Rigorous Bounds -- V. Brunn-Minkowski Inequality and Rearrangements -- V.1 A General Rearrangement Inequality for Multiple Integrals -- V.2 Some Inequalities for Gaussian Measures and the Long-Range Order of the One-Dimensional Plasma -- V.3 Best Constants in Youngโs Inequality, Its Converse and Its Generalization to More than Three Functions -- V.4 On Extensions of the Brunn-Minkowski and Prรฉkopa-Leindler Theorems, Including Inequalities for Log Concave Functions and with an Application to the Diffusion Equation -- V.5 Existence and Uniqueness of the Minimizing Solution of Choquardโs Nonlinear Equation -- V.6 Symmetric Decreasing Rearrangement Can Be Discontinuous -- V.7 The (Non) Continuity of Symmetric Decreasing Rearrangement -- V.8 On the Case of Equality in the Brunn-Minkowski Inequality for Capacity -- VI. General Analysis -- VI.1 An Lp Bound for the Riesz and Bessel Potentials of Orthonormal Functions -- VI.2 A Relation Between Pointwise Convergence of Functions and Convergence of Functionals -- VI.3 Sharp Constants in the Hardy-Littlewood-Sobolev and Related Inequalities -- VI.4 On the Lowest Eigenvalue of the Laplacian for the Intersection of Two Domains -- VI.5 Minimum Action Solutions of Some Vector Field Equations -- VI.6 Sobolev Inequalities with Remainder Terms (with H. Brezis) -- VI.7 Gaussian Kernels Have Only Gaussian Maximizers -- VI.8 Integral Bounds for Radar Ambiguity Functions and Wigner Distributions -- VII. Inequalities Related to Harmonic Maps -- VII.1 Estimations dโรฉnergie pour des applications de R3 ร valeurs dans S2 -- VII.2 Singularities of Energy Minimizing Maps from the Ball to the Sphere -- VII.3 Co-area, Liquid Crystals, and Minimal Surfaces -- VII.4 Counting Singularities in Liquid Crystals (with F. Almgren) -- VII.5 Symmetry of the Ginzburg-Landau Minimizer in a Disc -- Publications of Elliott H. Lieb