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Harmonic analysis of covariant functions of characters of normal subgroups.
- Source :
-
Proceedings of the American Mathematical Society . Jul2023, Vol. 151 Issue 7, p2919-2933. 15p. - Publication Year :
- 2023
-
Abstract
- This paper considers L^1-spaces of covariant functions of characters of normal subgroups. Assume that G is a locally compact group with the group algebra L^1(G) and N is a closed and normal subgroup of G. Suppose that \mathbb {T} is the circle group and \xi :N\to \mathbb {T} is a character. We introduce the Banach space L_\xi ^1(G,N) of covariant functions of \xi on G and present an operator theoretic approach to study structure of L^1_\xi (G,N). It is proven that L^1_\xi (G,N) and a quotient space of L^1(G) are isometrically isomorphic. The paper is concluded by constructive characterizations for covariant functions of \xi. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00029939
- Volume :
- 151
- Issue :
- 7
- Database :
- Academic Search Index
- Journal :
- Proceedings of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 163280310
- Full Text :
- https://doi.org/10.1090/proc/16229