Shift-modulation invariant spaces on LCA groups

2011/09/02 by Carlos Cabrelli, Cabrelli, Carlos, Victoria Paternostro +1
Mathematics · #43A77 (Primary) 43A15 (Secondary) #Advanced Algebra and Geometry #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Mathematical Dynamics and Fractals #math.CA #msc:43A15 #msc:43A77

paper · pdf · doi:10.48550/arxiv.1109.0482

17 pages

openalex publication_date 2011/09/02 · arxiv created 2012/06/05 · arxiv updated 2012/06/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

A (K,Λ) shift-modulation invariant space is a subspace of L²(G), that is invariant by 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 G, respectively. In this article we provide a characterization of shift-modulation invariant spaces in this general context when K and Λ are uniform lattices. This extends previous results known for L²(\R^d). We develop fiberization techniques and suitable range functions adapted to LCA groups needed to provide the desired characterization.

Related

• Shift Invariant Spaces on LCA Groups
• Extra Invariance of Shift-Invariant Spaces on LCA Groups
• Modulation invariant spaces on locally compact abelian groups
• Extra invariance of principal shift invariant spaces and the Zak transform
• Approximation by group invariant subspaces