Abstract
Let S be an abelian * - semigroup in double-struck Q signk. We give a sufficient condition for every positive definite function on S to have a unique representing measure on the dual semigroup of 5 (i. e. S is perfect). To characterize perfectness for any abelian * - semigroup is a challenging, but not yet generally solved problem. In this paper, we characterize the structure of involutions on an abelian * - semigroup which is a subset of double-struck Q signk, and show that any conelike * - semigroups in double-struck Q signk are perfect.
| Original language | English |
|---|---|
| Pages (from-to) | 155-167 |
| Number of pages | 13 |
| Journal | Mathematische Nachrichten |
| Volume | 216 |
| Publication status | Published - 2000 |
| Externally published | Yes |
Keywords
- * - semigroup
- Conelike
- Moment
- Perfect
- Positive definite
ASJC Scopus subject areas
- Mathematics(all)
Cite this
Perfectness of conelike * - Semigroups in double-struck Q signk. / Nishio, Katsuyoshi; Sakakibara, Nobuhisa.
In: Mathematische Nachrichten, Vol. 216, 2000, p. 155-167.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Perfectness of conelike * - Semigroups in double-struck Q signk
AU - Nishio, Katsuyoshi
AU - Sakakibara, Nobuhisa
PY - 2000
Y1 - 2000
N2 - Let S be an abelian * - semigroup in double-struck Q signk. We give a sufficient condition for every positive definite function on S to have a unique representing measure on the dual semigroup of 5 (i. e. S is perfect). To characterize perfectness for any abelian * - semigroup is a challenging, but not yet generally solved problem. In this paper, we characterize the structure of involutions on an abelian * - semigroup which is a subset of double-struck Q signk, and show that any conelike * - semigroups in double-struck Q signk are perfect.
AB - Let S be an abelian * - semigroup in double-struck Q signk. We give a sufficient condition for every positive definite function on S to have a unique representing measure on the dual semigroup of 5 (i. e. S is perfect). To characterize perfectness for any abelian * - semigroup is a challenging, but not yet generally solved problem. In this paper, we characterize the structure of involutions on an abelian * - semigroup which is a subset of double-struck Q signk, and show that any conelike * - semigroups in double-struck Q signk are perfect.
KW - - semigroup
KW - Conelike
KW - Moment
KW - Perfect
KW - Positive definite
UR - http://www.scopus.com/inward/record.url?scp=0040518126&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0040518126&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:0040518126
VL - 216
SP - 155
EP - 167
JO - Mathematische Nachrichten
JF - Mathematische Nachrichten
SN - 0025-584X
ER -