Nonexistence in General of a Definitizing Ideal of the Desired Codimension

Nonexistence in General of a Definitizing Ideal of the Desired Codimension Positivity 7: 297–302, 2003. © 2003 Kluwer Academic Publishers. Printed in the Netherlands. Nonexistence in General of a Definitizing Ideal of the Desired Codimension 1 2 TORBEN MAACK BISGAARD and HORIA CORNEAN Nandrupsvej 7 st. th., DK-2000 Frederiksberg C, Denmark. E-mail: torben.bisgaard@get2net.dk Department of Mathematical Sciences, Frederik Bajersvej 7G, DK-9220 Aalborg Ø, Denmark. E-mail: cornean@math.auc.dk Received 19 March 2001; accepted 11 February 2002 1. Introduction Suppose (S, ·, ∗) is a semigroup equipped with an involution, that is, a mapping ∗ ∗ ∗ ∗ ∗ ∗ x → x : S → S such that (x ) = x and (xy) = y x for all x, y ∈ S.For subsets X and Y of S,define XY ={xy|x ∈ X, y ∈ T }. A function ϕ : SS → C is positive definite if c c ϕ(s s )  0 j k j j,k=1 for every choice of n ∈ N, s ,... ,s ∈ S,and c ,... ,c ∈ C. Positive definite 1 n 1 n ∗ −1 ∗ functions on abelian groups with the inverse involution (x = x ,or x =−x if composition is written additively) play a prominent rôle in probability theory since http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

Nonexistence in General of a Definitizing Ideal of the Desired Codimension

Loading next page...
 
/lp/springer_journal/nonexistence-in-general-of-a-definitizing-ideal-of-the-desired-BGBwUZ0tqB
Publisher
Kluwer Academic Publishers
Copyright
Copyright © 2003 by Kluwer Academic Publishers
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1023/A:1026230232413
Publisher site
See Article on Publisher Site

Abstract

Positivity 7: 297–302, 2003. © 2003 Kluwer Academic Publishers. Printed in the Netherlands. Nonexistence in General of a Definitizing Ideal of the Desired Codimension 1 2 TORBEN MAACK BISGAARD and HORIA CORNEAN Nandrupsvej 7 st. th., DK-2000 Frederiksberg C, Denmark. E-mail: torben.bisgaard@get2net.dk Department of Mathematical Sciences, Frederik Bajersvej 7G, DK-9220 Aalborg Ø, Denmark. E-mail: cornean@math.auc.dk Received 19 March 2001; accepted 11 February 2002 1. Introduction Suppose (S, ·, ∗) is a semigroup equipped with an involution, that is, a mapping ∗ ∗ ∗ ∗ ∗ ∗ x → x : S → S such that (x ) = x and (xy) = y x for all x, y ∈ S.For subsets X and Y of S,define XY ={xy|x ∈ X, y ∈ T }. A function ϕ : SS → C is positive definite if c c ϕ(s s )  0 j k j j,k=1 for every choice of n ∈ N, s ,... ,s ∈ S,and c ,... ,c ∈ C. Positive definite 1 n 1 n ∗ −1 ∗ functions on abelian groups with the inverse involution (x = x ,or x =−x if composition is written additively) play a prominent rôle in probability theory since

Journal

PositivitySpringer Journals

Published: Oct 17, 2004

References

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

DeepDyve Freelancer

DeepDyve Pro

Price
FREE
$49/month

$360/year
Save searches from Google Scholar, PubMed
Create lists to organize your research
Export lists, citations
Read DeepDyve articles
Abstract access only
Unlimited access to over
18 million full-text articles
Print
20 pages/month
PDF Discount
20% off