Geodesic
Spectral synthesis in $L^2(G)$
Jean Ludwig 1   ; Carine Molitor-Braun 2   ; Sanjoy Pusti 3
1 Université de Lorraine Institut Élie Cartan de Lorraine UMR 7502 F-57045 Metz, France
2 Mathematics Research Unit University of Luxembourg Campus Kirchberg 6, rue Richard Coudenhove-Kalergi L-1359, Luxembourg
3 Mathematics Research Unit University of Luxembourg Campus Kirchberg 6, rue Richard Coudenhove-Kalergi L-1359, Luxembourg and Department of Mathematics and Statistics Indian Institute of Technology Kanpur, India 208016
Colloquium Mathematicum, Tome 138 (2015) no. 1, pp. 89-103 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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For locally compact, second countable, type I groups $G$, we characterize all closed (two-sided) translation invariant subspaces of $L^2(G)$. We establish a similar result for $K$-biinvariant $L^2$-functions ($K$ a fixed maximal compact subgroup) in the context of semisimple Lie groups.
DOI : 10.4064/cm138-1-6
Keywords: locally compact second countable type groups characterize closed two sided translation invariant subspaces establish similar result k biinvariant functions fixed maximal compact subgroup context semisimple lie groups

Jean Ludwig  1   ; Carine Molitor-Braun  2   ; Sanjoy Pusti  3

1 Université de Lorraine Institut Élie Cartan de Lorraine UMR 7502 F-57045 Metz, France
2 Mathematics Research Unit University of Luxembourg Campus Kirchberg 6, rue Richard Coudenhove-Kalergi L-1359, Luxembourg
3 Mathematics Research Unit University of Luxembourg Campus Kirchberg 6, rue Richard Coudenhove-Kalergi L-1359, Luxembourg and Department of Mathematics and Statistics Indian Institute of Technology Kanpur, India 208016 
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Jean Ludwig; Carine Molitor-Braun; Sanjoy Pusti. Spectral synthesis in $L^2(G)$. Colloquium Mathematicum, Tome 138 (2015) no. 1, pp. 89-103. doi: 10.4064/cm138-1-6

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