Shift-modulation invariant spaces on LCA groups

Carlos Cabrelli¹ ; Victoria Paternostro²

¹ Departamento de Matemática Facultad de Ciencias Exactas y Naturales Universidad de Buenos Aires Ciudad Universitaria, Pabellón I 1428 Buenos Aires, Argentina and IMAS-CONICET Consejo Nacional de Investigaciones Científicas y Técnicas Argentina
² Departamento de Matemática Facultad de Ciencias Exactas y Naturales Universidad de Buenos Aires Ciudad Universitaria, Pabellón I 1428 Buenos Aires, Argentina

Studia Mathematica, Tome 211 (2012) no. 1, pp. 1-19

Résumé

A $(K,\varLambda )$ shift-modulation invariant space is a subspace of $L^2(G)$ that is invariant under translations along elements in $K$ and modulations by elements in $\varLambda $. Here $G$ is a locally compact abelian group, and $K$ and $\varLambda $ are closed subgroups of $G$ and the dual group $\hat G$, respectively.We provide a characterization of shift-modulation invariant spaces when $K$ and $\varLambda $ are uniform lattices. This extends previous results known for $L^2(\mathbb R^d)$. We develop fiberization techniques and suitable range functions adapted to LCA groups needed to provide the desired characterization.

Détail

DOI : 10.4064/sm211-1-1

Keywords: varlambda shift modulation invariant space subspace invariant under translations along elements modulations elements varlambda here locally compact abelian group and varlambda closed subgroups dual group hat respectively provide characterization shift modulation invariant spaces varlambda uniform lattices extends previous results known mathbb develop fiberization techniques suitable range functions adapted lca groups needed provide desired characterization