5 papers
The Hörmander--Bernhardsson function in higher dimensions
Felipe Gonçalves, Danylo Radchenko, Antonio Pedro Ramos
We study the problem of finding the norm of the point evaluation operator in the Paley--Wiener space $PW^{1}(\r^d)$, consisting of -variable functions of spherical exponential t…
Sharp Lower Bounds for Sumsets in Hypercubes
Felipe Gonçalves, Danylo Radchenko
We prove a sharp lower bound for the cardinality of sumsets of subsets of confined to a hypercube, resolving in strong form a conjecture that was made explicit by Be…
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 f…
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…