Power Search
Low Price Guarantee
We Take School POs
Asymptotic Theory of Finite Dimensional Normed Spaces: Isoperimetric Inequalities in Riemannian Manifolds Corr Print Edition
Contributor(s): Milman, Vitali D. (Author), Schechtman, Gideon (Author)

View larger image

 ISBN: 3540167692     ISBN-13: 9783540167693
Publisher: Springer
OUR PRICE: $42.74  

Binding Type: Paperback
Published: July 1986
Qty:

Annotation: Vol. 1200 of the LNM series deals with the geometrical structure of finite dimensional normed spaces. One of the main topics is the estimation of the dimensions of euclidean and ln p spaces which nicely embed into diverse finite-dimensional normed spaces. An essential method here is the concentration of measure phenomenon which is closely related to large deviation inequalities in Probability on the one hand, and to isoperimetric inequalities in Geometry on the other.
The book contains also an appendix, written by M. Gromov, which is an introduction to isoperimetric inequalities on riemannian manifolds. Only basic knowledge of Functional Analysis and Probability is expected of the reader. The book can be used (and was used by the authors) as a text for a first or second graduate course. The methods used here have been useful also in areas other than Functional Analysis (notably, Combinatorics).

Click for more in this series: Lecture Notes in Mathematics
Additional Information
BISAC Categories:
- Mathematics | Transformations
- Mathematics | Mathematical Analysis
- Mathematics | Geometry - Analytic
Dewey: 515.73
LCCN: 86017871
Series: Lecture Notes in Mathematics
Physical Information: 0.37" H x 6.14" W x 9.21" L (0.55 lbs) 160 pages
 
Descriptions, Reviews, Etc.
Publisher Description:
This book deals with the geometrical structure of finite dimensional normed spaces, as the dimension grows to infinity. This is a part of what came to be known as the Local Theory of Banach Spaces (this name was derived from the fact that in its first stages, this theory dealt mainly with relating the structure of infinite dimensional Banach spaces to the structure of their lattice of finite dimensional subspaces). Our purpose in this book is to introduce the reader to some of the results, problems, and mainly methods developed in the Local Theory, in the last few years. This by no means is a complete survey of this wide area. Some of the main topics we do not discuss here are mentioned in the Notes and Remarks section. Several books appeared recently or are going to appear shortly, which cover much of the material not covered in this book. Among these are Pisier's Pis6] where factorization theorems related to Grothendieck's theorem are extensively discussed, and Tomczak-Jaegermann's T-Jl] where operator ideals and distances between finite dimensional normed spaces are studied in detail. Another related book is Pietch's Pie].
 
Customer ReviewsSubmit your own review
 
To tell a friend about this book, you must Sign In First!