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Perturbed interpolation formulae and applications

João P. G. Ramos and Mateus Sousa

Vol. 16 (2023), No. 10, 2327–2384
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 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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