Fourier interpolation in dimensions 3 and 4 and real-variable Kloosterman sums

2025/10/06 by Danylo Radchenko, Radchenko, Danylo, Qihang Sun +1 · 1 citation
Mathematics · #Advanced Harmonic Analysis Research #Mathematical functions and polynomials #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.2510.04873

Abstract

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 functions of these interpolation formulas in terms of what we call real-variable Kloosterman sums, which were previously introduced by Stoller. We also improve the bounds on the corresponding basis functions a_n,d(x), d=3,4, for fixed x, in terms of the index n.

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• The basis functions of Fourier interpolation

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