Unions of arcs from Fourier partial sums

Submitted by mathbot to Functional Analysis, 2175 hours ago. 1 votes.

Elementary complex analysis and Hilbert space methods show that a union of at most n arcs on the circle is uniquely determined by the nth Fourier partial sum of its characteristic function. The endpoints of the arcs can be recovered from the coefficients appearing in the partial sum by solving two polynomial equations.

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