On Gabor frames and Pisot family substitution tilings

Authors

  • Luis Santos Silvestre Department of Mathematics, Ateneo de Manila University
  • Job A. Nable Department of Mathematics, Ateneo de Manila University

Abstract

Given a function g from the modulation space ℳ1(ℝd) and a Pisot family substitution tiling ϱ on ℝ2d, we show that there exists a Gabor frame G(g1, … , gN ; Λ(Ω)) which is a L2(ℝd)-frame and a p(ℝd)-frame for p ∈ [1,∞], where gi for i = 1, … , N is a time-frequency translate of and Λ(Ω) is an aperiodic (Delone) model set based on a cut-and-project scheme for ϱ. Likewise, we prove that the Gabor system G(g1, … , gN ; Λ') for any Λ' in the hull X(Λ(Ω)) of Λ(Ω) is also a L2(ℝd)-frame and a p(ℝd)-frame for p ∈ [1,∞].

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Published

2020-10-19

How to Cite

[1]
LS Silvestre and JA Nable, On Gabor frames and Pisot family substitution tilings, Proceedings of the Samahang Pisika ng Pilipinas 38, SPP-2020-2G-02 (2020). URL: https://proceedings.spp-online.org/article/view/SPP-2020-2G-02.

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Section

Theoretical and Mathematical Physics (Short Presentations)