Other available formats:
Looking for an examination copy?
This title is not currently available for examination. However, if you are interested in the title for your course we can consider offering an examination copy. To register your interest please contact email@example.com providing details of the course you are teaching.
Convexity is important in theoretical aspects of mathematics and also for economists and physicists. In this monograph the author provides a comprehensive insight into convex sets and functions including the infinite-dimensional case and emphasizing the analytic point of view. Chapter one introduces the reader to the basic definitions and ideas that play central roles throughout the book. The rest of the book is divided into four parts: convexity and topology on infinite-dimensional spaces; Loewner's theorem; extreme points of convex sets and related issues, including the Krein–Milman theorem and Choquet theory; and a discussion of convexity and inequalities. The connections between disparate topics are clearly explained, giving the reader a thorough understanding of how convexity is useful as an analytic tool. A final chapter overviews the subject's history and explores further some of the themes mentioned earlier. This is an excellent resource for anyone interested in this central topic.Read more
- The first monograph to comprehensively cover inequalities related to convexity
- Covers a large number of topics unavailable in the monograph literature
- Includes a detailed discussion of Choquet theory, essential for all analysts
Reviews & endorsements
"Simon's monograph is a valuable addition to the literature on convexity that will inspire many minds enchanted by the beauty and power of the cornerstone of functional analysis."
S. Kutateladze, Mathematical Reviews
Not yet reviewed
Be the first to review
Review was not posted due to profanity×
- Date Published: June 2011
- format: Hardback
- isbn: 9781107007314
- length: 356 pages
- dimensions: 231 x 157 x 25 mm
- weight: 0.64kg
- contains: 8 b/w illus.
- availability: Available
Table of Contents
1. Convex functions and sets
2. Orlicz spaces
3. Gauges and locally convex spaces
4. Separation theorems
5. Duality: dual topologies, bipolar sets, and Legendre transforms
6. Monotone and convex matrix functions
7. Loewner's theorem: a first proof
8. Extreme points and the Krein–Milman theorem
9. The strong Krein–Milman theorem
10. Choquet theory: existence
11. Choquet theory: uniqueness
12. Complex interpolation
13. The Brunn–Minkowski inequalities and log concave functions
14. Rearrangement inequalities: a) Brascamp–Lieb–Luttinger inequalities
15. Rearrangement inequalities: b) Majorization
16. The relative entropy
Sorry, this resource is locked
Please register or sign in to request access. If you are having problems accessing these resources please email firstname.lastname@example.orgRegister Sign in
You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner www.ebooks.com. Please see the permission section of the www.ebooks.com catalogue page for details of the print & copy limits on our eBooks.Continue ×
Are you sure you want to delete your account?
This cannot be undone.
Thank you for your feedback which will help us improve our service.
If you requested a response, we will make sure to get back to you shortly.×