Higher order monotonic (multi-) sequences and their extreme points

Higher order monotonic (multi-) sequences and their extreme points Functions on the half-line which are non-negative and decreasing of a higher order have a long tradition. When normalized they form a simplex whose extreme points are well-known. For functions on $${\mathbb{N}_{0} = \{0, 1, 2, . . .\}}$$ the situation is different. Since an n-monotone sequence is in general not the restriction of an n-monotone function on $${\mathbb{R}_{+}}$$ (apart from n = 1 and n = 2), it is not even clear at the beginning if the normalized n-monotone sequences form a simplex. We will show in this paper that this is actually true, and we determine their extreme points. A corresponding result will also be proved for multi-sequences. The main ingredient in the proof will be a relatively new characterization of so-called survival functions of probability measures on (subsets of) $${\mathbb{R}^n}$$ , in this case on $${\mathbb{N}^{n}_{0}}$$ . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

Higher order monotonic (multi-) sequences and their extreme points

Positivity , Volume 17 (2) – Mar 14, 2012

Loading next page...
SP Birkhäuser Verlag Basel
Copyright © 2012 by Springer Basel AG
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
Publisher site
See Article on Publisher Site


You’re reading a free preview. Subscribe to read the entire article.

DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 12 million articles from more than
10,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Unlimited reading

Read as many articles as you need. Full articles with original layout, charts and figures. Read online, from anywhere.

Stay up to date

Keep up with your field with Personalized Recommendations and Follow Journals to get automatic updates.

Organize your research

It’s easy to organize your research with our built-in tools.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

Monthly Plan

  • Read unlimited articles
  • Personalized recommendations
  • No expiration
  • Print 20 pages per month
  • 20% off on PDF purchases
  • Organize your research
  • Get updates on your journals and topic searches


Start Free Trial

14-day Free Trial

Best Deal — 39% off

Annual Plan

  • All the features of the Professional Plan, but for 39% off!
  • Billed annually
  • No expiration
  • For the normal price of 10 articles elsewhere, you get one full year of unlimited access to articles.



billed annually
Start Free Trial

14-day Free Trial