Fourier interpolation and time-frequency localization

2020/05/26 by Kulikov, Aleksei · 2 citations
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2005.12836

Abstract

We prove that under very mild conditions for any interpolation formula f(x) = ∑_{λ∈ Λ} f(λ)a_λ(x) + ∑_{μ∈ M} f(μ)b_μ(x) we have a lower bound for the counting functions n_Λ(R₁) + n_M(R₂) ≥ 4R₁R₂ - Clog^2+ε(4R₁R₂) which very closely matches interpolation formulas discovered by Radchenko and Viazovska and by Bondarenko, Radchenko and Seip.

Cited by

• The basis functions of Fourier interpolation
• Critical and asymmetric Fourier uniqueness pairs

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