Fourier interpolation on the real line

Radchenko, Danylo; Viazovska, Maryna

doi:10.1007/s10240-018-0101-z

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Fourier interpolation on the real line

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Radchenko, Danylo
Max Planck Institute for Mathematics, Max Planck Society;

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Viazovska, Maryna
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1007/s10240-018-0101-z
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arXiv:1701.00265.pdf
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Citation

Radchenko, D., & Viazovska, M. (2019). Fourier interpolation on the real line. Publications mathématiques de l'IHÉS, 129(1), 51-81. doi:10.1007/s10240-018-0101-z.

Cite as: https://hdl.handle.net/21.11116/0000-0004-8AAE-D

Abstract

In this paper we construct an explicit interpolation formula for Schwartz functions on the real line. The formula expresses the value of a function at any given point in terms of the values of the function and its Fourier transform on the set $\{0,\pm\sqrt{1}, \pm\sqrt{2}, \pm\sqrt{3},\dots\}$. The functions in the interpolating basis are constructed in a closed form as an integral transform of weakly holomorphic modular forms for the theta subgroup of the modular group.