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alpha-POSITIVE/alpha-NEGATIVE DEFINITE FUNCTIONS ON GROUPS

Title
alpha-POSITIVE/alpha-NEGATIVE DEFINITE FUNCTIONS ON GROUPS
Author
허재성
Keywords
alpha-positive/alpha-negative definite function; Krein space; J-representation; J-cocycle; proper (alpha, J)-action
Issue Date
2018-05
Publisher
ROCKY MT MATH CONSORTIUM
Citation
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, v. 48, no. 1, page. 249-268
Abstract
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.
URI
https://projecteuclid.org/euclid.rmjm/1524880890http://repository.hanyang.ac.kr/handle/20.500.11754/118789
ISSN
0035-7596; 1945-3795
DOI
10.1216/RMJ-2018-48-1-249
Appears in Collections:
COLLEGE OF NATURAL SCIENCES[S](자연과학대학) > MATHEMATICS(수학과) > Articles
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