论文标题
傅里叶综合中的Hölder-logarithmic稳定性
Hölder-logarithmic stability in Fourier synthesis
论文作者
论文摘要
我们证明了hölder-logarithmic稳定性估算值，即从其傅立叶变换$ \ mathcal $ \ mathcal {f} v $上找到足够规则的紧凑型功能$ v $ $ \ mathbb {r}^d $。该估计依赖于$ \ Mathcal {f} v $从$ [ - r，r，r]^d $的Hölder稳定延续到较大的域。相关的重建程序基于一系列Chebyshev多项式。我们还提供了一个明确的示例，显示了我们的稳定性估计值的最佳性。
We prove a Hölder-logarithmic stability estimate for the problem of finding a sufficiently regular compactly supported function $v$ on $\mathbb{R}^d$ from its Fourier transform $\mathcal{F} v$ given on $[-r,r]^d$. This estimate relies on a Hölder stable continuation of $\mathcal{F}v$ from $[-r,r]^d$ to a larger domain. The related reconstruction procedures are based on truncated series of Chebyshev polynomials. We also give an explicit example showing optimality of our stability estimates.
