Perturbed interpolation formulae and applications
arXiv:2005.10337 · doi:10.2140/apde.2023.16.2327
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.
arXiv comment53 pages
References in corpus (8)
- The sphere packing problem in dimension 24
- The sphere packing problem in dimension 8
- Quasicrystals and Poisson's summation formula
- Gaussian Subordination for the Beurling-Selberg Extremal Problem
- Fourier interpolation on the real line
- Stable polynomials and crystalline measures
- New Sign Uncertainty Principles
- Kadec-1/4 Theorem for Sinc Bases