Lectures on Analysis on Metric Spaces (Universitext)

Heinonen, Juha

ISBN 10: 1461265258 / ISBN 13: 9781461265252

Edité par Springer, 2012

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Détails bibliographiques

Titre : Lectures on Analysis on Metric Spaces (...

Éditeur : Springer

Date d'édition : 2012

Reliure : Couverture souple

Etat : Good

A propos de ce titre

Synopsis :

Analysis is an outgrowth of calculus which considers functions defined in Euclidean spaces which have derivatives. The theory of distributions and Sobolev spaces allowed mathematicians to extend these ideas to functions which were no longer differentiable. Recent developments in complex analysis have permitted researchers to replace Euclidean spaces by general metric spaces. The author is a great expositor and gives a first taste of this exciting new area.

Présentation de l'éditeur:

The purpose of this book is to communicate some of the recent advances in this field while preparing the reader for more advanced study. The material can be roughly divided into three different types: classical, standard but sometimes with a new twist, and recent. The author first studies basic covering theorems and their applications to analysis in metric measure spaces. This is followed by a discussion on Sobolev spaces emphasizing principles that are valid in larger contexts. The last few sections of the book present a basic theory of quasisymmetric maps between metric spaces. Much of the material is recent and appears for the first time in book format.