허재성
2019-12-08T04:58:51Z
2019-12-08T04:58:51Z
2018-05
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, v. 48, no. 1, page. 249-268
0035-7596
1945-3795
https://projecteuclid.org/euclid.rmjm/1524880890
https://repository.hanyang.ac.kr/handle/20.500.11754/118789
In this paper, we introduce the notions of an alpha-positive/alpha-negative definite function on a (discrete) group. We first construct the Naimark-GNS type representation associated to an alpha-positive definite function and prove the Schoenberg type theorem for a matricially bounded alpha-negative definite function. Using a J-representation on a Krein space (K, J) associated to a nonnegative normalized alpha-negative definite function, we also construct a J-cocycle associated to a J-representation. Using a J-cocycle, we show that there exist two sequences of alpha-positive definite functions and proper (alpha, J)-actions on a Krein space (K, J) corresponding to a proper matricially bounded a-negative definite function.
This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF), funded by the Ministry of Science, ICT and Future Planning, grant No. 2014029581.
en_US
ROCKY MT MATH CONSORTIUM
alpha-positive/alpha-negative definite function
Krein space
J-representation
J-cocycle
proper (alpha, J)-action
alpha-POSITIVE/alpha-NEGATIVE DEFINITE FUNCTIONS ON GROUPS
Article
1
48
10.1216/RMJ-2018-48-1-249
249-268
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS
Heo, Jaeseong
2018006775
S
COLLEGE OF NATURAL SCIENCES[S]
DEPARTMENT OF MATHEMATICS
hjs