Weyl-Heisenberg Frame Wavelets with Basic Supports

2005/07/29 by Xunxiang Guo, Guo, Xunxiang, Yuanan Diao +3
Mathematics · #42C99 #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #math.FA #msc:42C99

paper · pdf · doi:10.48550/arxiv.math/0507609

11 pages, 2 figures

arxiv created 2005/07/29 · openalex publication_date 2005/07/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let a, b be two fixed non-zero constants. A measurable set E⊂ ℝ is called a Weyl-Heisenberg frame set for (a, b) if the function g=χ_E generates a Weyl-Heisenberg frame for L²(ℝ) under modulates by b and translates by a, i.e., \e^imbtg(t-na\_m,n∈ℤ is a frame for L²(ℝ). It is an open question on how to characterize all frame sets for a given pair (a,b) in general. In the case that a=2π and b=1, a result due to Casazza and Kalton shows that the condition that the set F=\bigcup_j=1^k([0,2π)+2n_jπ) (where \n₁

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