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.
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Radchenko, D., Viazovska, M. Fourier interpolation on the real line. Publ.math.IHES 129, 51–81 (2019). https://doi.org/10.1007/s10240-018-0101-z
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DOI: https://doi.org/10.1007/s10240-018-0101-z