"Fourier interpolation formulas, uniqueness pairs, and energy minimization problems"Radchenko, DanyloI will discuss some recently discovered formulas that allow one to reconstruct any sufficiently nice function from discrete samples of its values and the values of its Fourier transform. Curiously, these interpolation formulas are intimately connected to the theory of modular forms for the principal congruence subgroup of level 2 in PSL2(Z). I will also discuss the connection of these results to the energy minimization problem in Euclidean spaces and some related open questions. |
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