Perturbed interpolation formulae and applications

TL;DR

This paper uses functional analysis to perturb classical Fourier interpolation results, leading to generalized theorems and new applications in Fourier analysis and interpolation formulae.

Contribution

It introduces a novel perturbation approach to classical Fourier interpolation results, extending their applicability in various settings.

Findings

Generalized Kadec's 1/4-theorem for Paley-Wiener spaces

Perturbation of Radchenko-Viazovska interpolation results

Applications to Fourier interpolation with derivatives in dimensions 8 and 24

Abstract

We employ functional analysis techniques in order to deduce that some classical and recent interpolation results in Fourier analysis can be suitably perturbed. As an application of our techniques, we obtain generalizations of Kadec's 1/4-theorem for interpolation formulae in the Paley-Wiener space both in the real and complex case, as well as a perturbation result on the recent Radchenko-Viazovska interpolation result and the Cohn-Kumar-Miller-Radchenko-Viazovska result for Fourier interpolation with derivatives in dimensions 8 and 24. We also provide several applications of the main results and techniques, all relating to recent contributions in interpolation formulae and uniqueness sets for the Fourier transform.