Weighted Zak transforms and the dual tiling condition

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:487

Article

Lee, Dae Gwan¹  Pfander, Goetz E.¹ 

[1] Kathol Univ Eichstatt Ingolstadt, Math Geograph Fak, D-85071 Eichstatt, Germany

关键词: Zak transform;    Time-frequency analysis;    Dual tiling condition;   

DOI  :  10.1016/j.jmaa.2020.124020

来源: Elsevier

【 摘 要 】

For T > 0 and a periodic complex-valued sequence c, we introduce the weighted Zak transform Z(c)(T) and study its properties. As our main result, we give characterizations for mapping properties and unitarity of Z(c)(T) : L-2(R) -> L-2(S) where functions in the image are understood as restrictions to a set S subset of R-2. In particular, we show that for almost every choice of L-periodic sequences c, the mapping properties of Z(c)(T) : L-2(R) -> L-2(S) simplify to statements on the geometry of S. They involve a dual tiling condition on S with respect to the lattices TZx Omega Z and LTZxL Omega Z where Omega = 1/(LT). (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free