Abstract:
We will describe an interpolation formula for Schwartz eigenfunctions of the Fourier transform on the real line. The formula is related to the Whittaker-Shannon interpolation formula for band-limited functions, but uses square roots of integers instead of integers as sampling points. It turns out that the basis functions of this interpolation formula can be given explicitly in terms of certain weakly holomorphic modular forms of weights 1/2 and 3/2 and have several other remarkable properties.
The talk is based on a joint work with Maryna Viazovska.