论文标题
从球上的傅立叶变换重建的稳定性估计值
Stability estimates for reconstruction from the Fourier transform on the ball
论文作者
论文摘要
我们证明了Hölder-logarithmic稳定性估算的估计值，即在$ \ mathbb {r}^d $上找到可集成函数$ v $，并从INFINITY在其傅立叶变换$ \ mathcal $ \ mathcal {f} v $ of the the pall $ b_r $ b_r $上给出的超过指数衰减。这些估计值来自$ \ Mathcal {f} v $从$ b_r $到更大的球的Hölder稳定的外推。我们还提出了不稳定的例子，显示了我们的结果的最佳性。
We prove Hölder-logarithmic stability estimates for the problem of finding an integrable function $v$ on $\mathbb{R}^d$ with a super-exponential decay at infinity from its Fourier transform $\mathcal{F} v$ given on the ball $B_r$. These estimates arise from a Hölder-stable extrapolation of $\mathcal{F} v$ from $B_r$ to a larger ball. We also present instability examples showing an optimality of our results.
