Perturbed interpolation formulae and applications

Ramos, João P. G.; Sousa, Mateus

doi:10.2140/apde.2023.16.2327

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Perturbed interpolation formulae and applications

João P. G. Ramos and Mateus Sousa

Vol. 16 (2023), No. 10, 2327–2384

DOI: 10.2140/apde.2023.16.2327

Abstract

We employ functional analysis techniques in order to deduce some versions of classical and recent interpolation results in Fourier analysis with perturbed nodes. As an application of our techniques, we obtain generalizations of Kadec’s $\frac{1}{4}$ -theorem for interpolation formulae in the Paley–Wiener space both in the real and complex cases, as well as versions of the recent interpolation result of Radchenko and Viazovska (Publ. Math. Inst. Hautes Études Sci. 129 (2019), 51–81) and the result of Cohn, Kumar, Miller, Radchenko and Viazovska (Ann. Math $(2)$ 196:3 (2022), 983–1082) for Fourier interpolation with derivatives in dimensions $8$ and $24$ with suitable perturbations of the interpolation nodes. We also provide several applications of the main results and techniques, relating to recent contributions in interpolation formulae and uniqueness sets for the Fourier transform.

Keywords

interpolation formulae, band-limited functions, modular forms, invertible operators, Fourier transform

Mathematical Subject Classification

Primary: 41A05, 42A38

Secondary: 46E39, 11F30

Milestones

Received: 23 June 2021

Revised: 14 April 2022

Accepted: 28 May 2022

Published: 11 December 2023

Authors

João P. G. Ramos
Department of Mathematics ETH Zürich Zürich Switzerland

Mateus Sousa
Basque Center for Applied Mathematics Bilbao Spain

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Vol. 16, No. 10, 2023