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arXiv · 1701.00265

Fourier interpolation on the real line

Danylo Radchenko·Maryna Viazovska
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Abstract

We use weakly holomorphic modular forms for the Hecke theta group to 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 $\{0, \pm\sqrt{1}, \pm\sqrt{2}, \pm\sqrt{3},\dots\}$.

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Danylo Radchenko, Maryna Viazovska. 2020-02-14. Fourier interpolation on the real line. https://doi.org/10.1007/s10240-018-0101-z

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