Analysis

Elliott H. Lieb, Michael Loss

346 pages, parution le 01/05/2001 (2^eme édition)

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Résumé

Significantly revised and expanded, this new Second Edition provides readers at all levels--from beginning students to practicing analysts--with the basic concepts and standard tools necessary to solve problems of analysis, and how to apply these concepts to research in a variety of areas.

Authors Elliott Lieb and Michael Loss take you quickly from basic topics to methods that work successfully in mathematics and its applications. While omitting many usual typical textbook topics, Analysis includes all necessary definitions, proofs, explanations, examples, and exercises to bring the reader to an advanced level of understanding with a minimum of fuss, and, at the same time, doing so in a rigorous and pedagogical way. Many topics that are useful and important, but usually left to advanced monographs, are presented in Analysis, and these give the beginner a sense that the subject is alive and growing.

This new Second Edition incorporates numerous changes since the publication of the original 1997 edition and includes:

Features:

a new chapter on eigenvalues that covers the min-max principle, semi-classical approximation, coherent states, Lieb-Thirring inequalities, and more
extensive additions to chapters covering Sobolev Inequalities, including the Nash and Log Sobolev inequalities
new material on Measure and Integration
many new exercises
and much more ...

The Second Edition continues its no-nonsense approach to the topic that has made it one of the best selling books on the subject. It is an authoritative, straight-forward volume that readers--from the graduate student, to the professional mathematician, to the physicist or engineer using analytical methods--will find useful both as a reference and as a guide to real problem solving.

Contents

Measure and integration
L^p-spaces
Rearrangement inequalities
Integral inequalities
The Fourier transform
Distributions
The Sobolev spaces H¹ and H^1/2
Sobolev inequalities
Potential theory and Coulomb energies
Regularity of solutions of Poisson's equation
Introduction to the calculus of variations
More about eigenvalues
Part Title
List of symbols
References
Index

Caractéristiques techniques

	PAPIER
Éditeur(s)	American Mathematical Society (AMS)
Auteur(s)	Elliott H. Lieb, Michael Loss
Parution	01/05/2001
Édition	2^eme édition
Nb. de pages	346
Format	18 x 26
Couverture	Relié
Poids	963g
Intérieur	Noir et Blanc
EAN13	9780821827833
ISBN13	978-0-8218-2783-3