Skip to content
Register Sign in Wishlist

An Analytic Viewpoint

$105.00 (C)

Part of Cambridge Tracts in Mathematics

  • Author: Barry Simon, California Institute of Technology
  • Date Published: June 2011
  • availability: Available
  • format: Hardback
  • isbn: 9781107007314

$ 105.00 (C)

Add to cart Add to wishlist

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 providing details of the course you are teaching.

Product filter button
About the Authors
  • 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.

    • 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
    Read more

    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

    Customer reviews

    Not yet reviewed

    Be the first to review

    Review was not posted due to profanity


    , create a review

    (If you're not , sign out)

    Please enter the right captcha value
    Please enter a star rating.
    Your review must be a minimum of 12 words.

    How do you rate this item?


    Product details

    • 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
    17. Notes
    Author index
    Subject index.

  • Author

    Barry Simon, California Institute of Technology
    Barry Simon is IBM Professor of Mathematics and Theoretical Physics at the California Institute of Technology.

Sorry, this resource is locked

Please register or sign in to request access. If you are having problems accessing these resources please email

Register Sign in
Please note that this file is password protected. You will be asked to input your password on the next screen.

» Proceed

You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner Please see the permission section of the catalogue page for details of the print & copy limits on our eBooks.

Continue ×

Continue ×

Continue ×
warning icon

Turn stock notifications on?

You must be signed in to your Cambridge account to turn product stock notifications on or off.

Sign in Create a Cambridge account arrow icon

Find content that relates to you

Join us online

This site uses cookies to improve your experience. Read more Close

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.

Please fill in the required fields in your feedback submission.