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

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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

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