Geodesic
Article
Fourier interpolation on the real line
Publications Mathématiques de l'IHÉS, Tome 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 
@article{PMIHES_2019__129__51_0,
     author = {Radchenko, Danylo and Viazovska, Maryna},
     title = {Fourier interpolation on the real line},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     pages = {51--81},
     year = {2019},
     publisher = {Springer Berlin Heidelberg},
     address = {Berlin/Heidelberg},
     volume = {129},
     doi = {10.1007/s10240-018-0101-z},
     mrnumber = {3949027},
     zbl = {1455.11075},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s10240-018-0101-z/}
}
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AU  - Radchenko, Danylo
AU  - Viazovska, Maryna
TI  - Fourier interpolation on the real line
JO  - Publications Mathématiques de l'IHÉS
PY  - 2019
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EP  - 81
VL  - 129
PB  - Springer Berlin Heidelberg
PP  - Berlin/Heidelberg
UR  - http://geodesic.mathdoc.fr/articles/10.1007/s10240-018-0101-z/
DO  - 10.1007/s10240-018-0101-z
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%0 Journal Article
%A Radchenko, Danylo
%A Viazovska, Maryna
%T Fourier interpolation on the real line
%J Publications Mathématiques de l'IHÉS
%D 2019
%P 51-81
%V 129
%I Springer Berlin Heidelberg
%C Berlin/Heidelberg
%U http://geodesic.mathdoc.fr/articles/10.1007/s10240-018-0101-z/
%R 10.1007/s10240-018-0101-z
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%F PMIHES_2019__129__51_0
Radchenko, Danylo; Viazovska, Maryna. Fourier interpolation on the real line. Publications Mathématiques de l'IHÉS, Tome 129 (2019), pp. 51-81. doi: 10.1007/s10240-018-0101-z

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