Frame set for shifted sinc-function

2023/09/12 by Belov, Yurii, Semenov, Andrei V. · 2 citations
#30D10 #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2309.05969

Abstract

We prove that frame set F_g for imaginary shift of sinc-function g(t)=(sinπb(t-iw))/(t-iw), b,w∈ℝ∖\0\ can be described as F_g=\(α,β): αβ≤ 1, β≤|b|\. In addition, we prove that F_g=\(α,β): αβ≤ 1 \ for window functions g of the form (1)/(t-iw)(1-∑_k=1^∞a_ke^{2πi b_k t}), such that ∑_{k≥ 1}|a_k|e^2π|w|b_k<1, wb_k<0.

Cited by

• Frames for compactly supported functions with irrational density
• Universal frame set for rational functions

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