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Explore Fourier uniqueness and interpolation pairs in this 56-minute lecture by Maryna Viazovska from EPFL. Delve into the concept of reconstructing functions from their restrictions and Fourier transforms on specific subsets of Euclidean space. Gain insights into recent advancements in explicit constructions and existence results for Fourier interpolation pairs, as well as corresponding interpolation formulas. Examine the conditions under which a function can be reconstructed from its restriction to set X and its Fourier transform's restriction to set Y, with a focus on identifying affirmative (X,Y) pairs.
