扰动傅立叶唯一性和插值导致更高的维度
Perturbed Fourier uniqueness and interpolation results in higher dimensions
摘要：
得到了新的Fourier插值和全维的-唯一性结果，推广了第一作者和M.苏萨和第二作者。我们表明，唯一的施瓦茨函数，连同其傅里叶变换，消失的表面上接近的原点为中心的领域，其半径是整数的平方根，是零函数。在径向情况下，这些曲面是具有扰动半径的球面，而在非径向情况下，它们可以是球面上的连续函数的图形。作为一个应用程序，我们翻译我们的扰动傅立叶唯一性结果扰动海森堡唯一性的双曲线，使用这些领域之间的相互关系介绍和研究巴肯，Hedenmalm，蒙特斯-罗德里格斯，Radchenko和Viazovska。
英文摘要：
We obtain new Fourier interpolation and -uniqueness results in all dimensions, extending methods and results by the first author and M. Sousa, and by the second author. We show that the only Schwartz function which, together with its Fourier transform, vanishes on surfaces close to the origin-centered spheres whose radius are square roots of integers, is the zero function. In the radial case, these surfaces are spheres with perturbed radii, while in the non-radial case, they can be graphs of continuous functions over the sphere. As an application, we translate our perturbed Fourier uniqueness results to perturbed Heisenberg uniqueness for the hyperbola, using the interrelation between these fields introduced and studied by Bakan, Hedenmalm, Montes-Rodriguez, Radchenko and Viazovska.
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