Inequalities: Selecta of Elliott H. LiebInequalities 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 which should become a standard source for further research. Together with the mathematical proofs the author also presents numerous applications to the calculus of variations and to many problems of quantum physics, in particular to atomic physics. |
Contents
I | 33 |
II | 43 |
III | 47 |
IV | 59 |
V | 63 |
VI | 67 |
VIII | 81 |
IX | 91 |
XXIX | 343 |
XXX | 357 |
XXXI | 365 |
XXXII | 375 |
XXXIII | 389 |
XXXIV | 401 |
XXXV | 415 |
XXXVI | 439 |
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Common terms and phrases
algebra assume boundary BRASCAMP classical co-area concave function conjecture consider convergence convex convex function Corollary Coulomb defined definition denote density matrix dimension dimensional E. H. Lieb eigenvalues ELLIOTT H energy entropy equality equation example exists fact fermion ferromagnetism finite function f ƒ and g Gaussian functions Gaussian kernels given Hamiltonian hence Hilbert space Hölder's inequality holds implies integral Lemma Let f linear lower bound Ly,n Math Mathematics measure minimizing nonnegative norm Note operator orthogonal orthonormal p₁ paper particles Phys Physics positive potential Princeton problem proof of Theorem properties prove quantum rearrangement inequality Remark replaced result right side satisfies Schrödinger sequence sharp constant singular Sobolev inequality solution spin subadditivity subspace Suppose theory trace trace class unique variables vector Young's inequality zero