Fourier interpolation on the real line

Abstract

We use weakly holomorphic modular forms for the Hecke theta group to 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 $\{0,\pm \sqrt{1},\pm \sqrt{2},\pm \sqrt{3},\dots \}$.

References in corpus (3)

• New upper bounds on sphere packings I
• The sphere packing problem in dimension 24
• The sphere packing problem in dimension 8

Cited by in corpus (11)

• High-dimensional sphere packing and the modular bootstrap
• Stable polynomials and crystalline measures
• Perturbed Fourier uniqueness and interpolation results in higher dimensions
• Perturbed interpolation formulae and applications
• Crystalline temperate distributions with uniformly discrete support and spectrum
• Eigenfunctions of the Fourier Transform with specified zeros
• Phaseless sampling on square-root lattices
• Taylor coefficients and zeroes of entire functions of exponential type
• Sphere Packings in Euclidean Space with Forbidden Distances
• Measures, modular forms, and summation formulas of Poisson type
• From sphere packing to Fourier interpolation