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The basis functions of Fourier interpolation
David Berghaus, Andriy Bondarenko, Danylo Radchenko +2
The basis functions of the Fourier interpolation formula of Radchenko and Viazovska, constructed by means of weakly holomorphic modular forms for the Hecke theta group, are entire…
Fourier interpolation in dimensions 3 and 4 and real-variable Kloosterman sums
Danylo Radchenko, Qihang Sun
We give a construction of radial Fourier interpolation formulas in dimensions 3 and 4 using Maass--Poincaré type series. As a corollary we obtain explicit formulas for the basis fu…
The Kirkwood-Dirac representation associated to the Fourier transform for finite abelian groups: positivity
Stephan De Bièvre, Christopher Langrenez, Danylo Radchenko
We construct and study the Kirkwood-Dirac (KD) representations naturally associated to the Fourier transform of finite abelian groups . We identify all pure KD-positive states a…