TY - JOUR
AU - 허재성
DA - 2018/05
PY - 2018
UR - https://projecteuclid.org/euclid.rmjm/1524880890
UR - https://repository.hanyang.ac.kr/handle/20.500.11754/118789
AB - 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.
PB - ROCKY MT MATH CONSORTIUM
KW - alpha-positive/alpha-negative definite function
KW - Krein space
KW - J-representation
KW - J-cocycle
KW - proper (alpha, J)-action
TI - alpha-POSITIVE/alpha-NEGATIVE DEFINITE FUNCTIONS ON GROUPS
IS - 1
VL - 48
DO - 10.1216/RMJ-2018-48-1-249
T2 - ROCKY MOUNTAIN JOURNAL OF MATHEMATICS
ER -