论文标题
傅立叶插值和时频定位
Fourier interpolation and time-frequency localization
论文作者
论文摘要
我们证明，在非常轻微的条件下，对于任何插值公式$ f（x）= \ sum_ {λ\inλ} f（λ）a_λ（x） + sum_ + sum_ {μ\ in m} \ hat {f} \ hat {f}（f}（μ）b_μ）b_（x）$，我们对数量的计数_2 4R_1R_2 -C \ log^{2+ \ Varepsilon}（4R_1R_2）$，与Radchenko和Viazovska和Bondarenko，Radchenko和Seip发现的插值非常匹配。
We prove that under very mild conditions for any interpolation formula $f(x) = \sum_{λ\in Λ} f(λ)a_λ(x) + \sum_{μ\in M} \hat{f}(μ)b_μ(x)$ we have a lower bound for the counting functions $n_Λ(R_1) + n_{M}(R_2) \ge 4R_1R_2 - C\log^{2+\varepsilon}(4R_1R_2)$ which very closely matches interpolation formulas discovered by Radchenko and Viazovska and by Bondarenko, Radchenko and Seip.
