2012/05/30 by Bradley Currey, Currey, Bradley, Azita Mayeli +3
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Advanced Differential Geometry Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Representation Theory (math.RT) #math.CA #math.FA #math.RT
paper · pdf · doi:10.48550/arxiv.1205.6530
17 pages, no figures. Keywords: Shift-invariant spaces, translation invariant spaces, nilpotent Lie groups; range function; periodization operator; fibers; frame and Reisz bases
arxiv created 2012/05/30 · openalex publication_date 2012/05/30 · arxiv updated 2012/05/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a simply connected nilpotent Lie group having unitary irreducible representations that are square-integrable modulo the center (SI/Z), we develop a notion of periodization on the group Fourier transform side, and use this notion to give a characterization of shift-invariant spaces in L2(N) in terms of range functions. We apply these results to study the structure of frame and Reisz families for shift-invariant spaces. We illustrate these results for the Heisenberg group as well as for other groups with SI/Z representations.