Ramos, Joao P. G.Stoller, Martin2022-06-202022-06-202022-06-202022-06-1510.1016/j.jfa.2022.109448https://infoscience.epfl.ch/handle/20.500.14299/188585WOS:000795160200012We obtain new Fourier interpolation and uniqueness results in all dimensions, extending methods and results by the first author and M. Sousa [11] and the second author [12]. We show that the only Schwartz function which, together with its Fourier transform, vanishes on surfaces close to the origin-centered spheres whose radii 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 applica-tion, 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 Via-zovska [1].(c) 2022 Published by Elsevier Inc.Mathematicsinvertible operatorsfourier interpolationmodular formsheisenberg uniqueness pairstext::journal::journal article::research article