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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 . 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.
Radchenko, Danylo 1 ; Viazovska, Maryna 1
@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},
publisher = {Springer Berlin Heidelberg},
address = {Berlin/Heidelberg},
volume = {129},
year = {2019},
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/}
}
TY - JOUR AU - Radchenko, Danylo AU - Viazovska, Maryna TI - Fourier interpolation on the real line JO - Publications Mathématiques de l'IHÉS PY - 2019 SP - 51 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 LA - en ID - PMIHES_2019__129__51_0 ER -
%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 %G en %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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