Analysis / Elliott H. Lieb, Michael Loss

Auteur principal : Lieb, Elliott H., 1932-, AuteurCo-auteur : Loss, Michael, 1954-, AuteurType de document : MonographieCollection : Graduate studies in mathematics, 14Langue : anglais.Pays: Etats Unis.Mention d'édition: 2nd editionÉditeur : Providence : American Mathematical Society, 2001Description : 1 vol. (XXII-346 p.) ; 26 cmISBN: 0821827839.ISSN: 1065-7339.Bibliographie : Bibliogr. p. 335-339. Index.Sujet MSC : 28-01, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to measure and integration
42-01, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to harmonic analysis on Euclidean spaces
26-01, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to real functions
46-01, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to functional analysis
49-01, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to calculus of variations and optimal control
En-ligne : Zentralblatt | MathSciNet Item type: Monographie
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From the Preface to the second edition:

“This second edition contains corrections and some fresh items. Chief among these is Chapter 12 in which we explain several topics concerning eigenvalues of the Laplacian and the Schrödinger operator, such as the min-max principle, coherent states, semiclassical approximation and how to use these to get bounds on eigenvalues and sums of eigenvalues. But there are other additions, too, such as more on Sobolev spaces (Chapter 8) including a compactness criterion, and Poincaré, Nash and logarithmic Sobolev inequalities. The latter two are applied to obtain smoothing properties of semigroups.

Chapter 1 (Measure and integration) has been supplemented with a discussion of the more usual approach to integration theory using simple functions, and how to make this even simpler by using ‘really simple functions’. Egoroff’s theorem has also been added. Several additions were made to Chapter 6 (Distributions) including one about the Yukawa potential.

There are, of course, many more exercises as well”.

Bibliogr. p. 335-339. Index

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