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Unions of arcs from Fourier partial sums

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.

preprint2010arXivOpen access
Dennis Courtney
math.FA
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Dennis Courtney

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