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Fourier interpolation on the real line
Publications Mathématiques de l'IHÉS, Volume 129 (2019), pp. 51-81
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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,±1,±2,±3,⋯}. 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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DOI: 10.1007/s10240-018-0101-z

Danylo Radchenko 1; Maryna Viazovska 1

1 
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     title = {Fourier interpolation on the real line},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     pages = {51--81},
     year = {2019},
     publisher = {Springer Berlin Heidelberg},
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Danylo Radchenko; Maryna Viazovska. Fourier interpolation on the real line. Publications Mathématiques de l'IHÉS, Volume 129 (2019), pp. 51-81. doi: 10.1007/s10240-018-0101-z

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