Shift-modulation invariant spaces on LCA groups

Carlos Cabrelli; Victoria Paternostro

Studia Mathematica, Tome 209 (2012), p. 1-19 / Harvested from The Polish Digital Mathematics Library

Résumé

A (K,Λ) shift-modulation invariant space is a subspace of L²(G) that is invariant under translations along elements in K and modulations by elements in Λ. Here G is a locally compact abelian group, and K and Λ are closed subgroups of G and the dual group Ĝ, respectively. We provide a characterization of shift-modulation invariant spaces when K and Λ are uniform lattices. This extends previous results known for $L ² (ℝ^{d})$ . We develop fiberization techniques and suitable range functions adapted to LCA groups needed to provide the desired characterization.

Publié le : 2012-01-01

Zbl 1269.43001

EUDML-ID : urn:eudml:doc:285748

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     title = {Shift-modulation invariant spaces on LCA groups},
     journal = {Studia Mathematica},
     volume = {209},
     year = {2012},
     pages = {1-19},
     zbl = {1269.43001},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm211-1-1}
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Carlos Cabrelli; Victoria Paternostro. Shift-modulation invariant spaces on LCA groups. Studia Mathematica, Tome 209 (2012) pp. 1-19. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm211-1-1/