2009/05/12 by Magalí Anastasio, Anastasio, Magalí, Carlos Cabrelli +3 · 1 citation
Mathematics · #42C15 #42C40 (Primary) #46C99 (Secondary) #Advanced Algebra and Geometry #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Holomorphic and Operator Theory #Mathematical Analysis and Transform Methods #math.CA #msc:42C15 #msc:42C40 #msc:46C99
paper · pdf · doi:10.48550/arxiv.0905.1933
20 pages, Some corrections were added. To appear in Complex Analysis and Operator Theory
openalex publication_date 2009/05/12 · arxiv created 2010/02/08 · arxiv updated 2010/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article we study invariance properties of shift-invariant spaces in higher dimensions. We state and prove several necessary and sufficient conditions for a shift-invariant space to be invariant under a given closed subgroup of \Rd, and prove the existence of shift-invariant spaces that are exactly invariant for each given subgroup. As an application we relate the extra invariance to the size of support of the Fourier transform of the generators of the shift-invariant space. This work extends recent results obtained for the case of one variable to several variables.