Abstract:A. We are looking at families of functions or measures on the torus (in dimension one and two) which are specified by a finite number of parameters N. The task, for a given family, is to look at a small number of Fourier coefficients of the object, at a set of locations that is predetermined and may depend only on N, and determine the object. We look at (a) the indicator functions of at most N intervals of the torus and (b) at sums of at most N complex point masses on the two-dimensional torus. In the first ca… Show more
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