Analysis / Elliott H. Lieb, Michael Loss

Auteur: Lieb, Elliott H. (1932-) - AuteurCo-auteur: Loss, Michael (1954-) - AuteurType de document: MonographieCollection: Graduate studies in mathematics ; 14Langue: anglaisPays: Etats UnisÉditeur: Providence : American Mathematical Society, 2001Edition: 2nd editionDescription: 1 vol. (XXII-346 p.) ; 26 cm ISBN: 0821827839 ; rel. Note: 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”.Bibliographie: Bibliogr. p. 335-339. Index. Sujets MSC: 28-01 Measure and integration -- Instructional exposition (textbooks, tutorial papers, etc.)
42-01 Harmonic analysis on Euclidean spaces -- Instructional exposition (textbooks, tutorial papers, etc.)
26-01 Real functions -- Instructional exposition (textbooks, tutorial papers, etc.)
46-01 Functional analysis -- Instructional exposition (textbooks, tutorial papers, etc.)
49-01 Calculus of variations and optimal control; optimization -- Instructional exposition (textbooks, tutorial papers, etc.)
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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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