Inequalities Selecta of Elliott H. Lieb
Inequalities play a fundamental role in Functional Analysis and it is widely recognized that finding them, especially sharp estimates, is an art. E. H. Lieb has discovered a host of inequalities that are enormously useful in mathematics as well as in physics. His results are collected in this book w...
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| Other Authors: | , |
| Format: | eBook |
| Language: | English |
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Berlin, Heidelberg
Springer Berlin Heidelberg
2002, 2002
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| Edition: | 1st ed. 2002 |
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| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 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 Schrödinger Hamiltonian and Their Relation to Sobolev Inequalities
- III.2 On Semi-Classical Bounds for Eigenvalues of Schrödinger Operators
- III.3 The Number of Bound States of One-Body Schrödinger 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 Schrödinger 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 Young’s Inequality, Its Converse and Its Generalization to More than Three Functions
- V.4 On Extensions of the Brunn-Minkowski and Prékopa-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 Choquard’s Nonlinear Equation
- 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
- 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 d’énergie pour des applications de R3 à valeurs dans S2
- 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 Simon’s 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