New York Journal of Mathematics
Volume 16 (2010) 235-243


Dennis Courtney

Unions of arcs from Fourier partial sums

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Published: October 20, 2010
Keywords: Fourier coefficients, trigonometric moment problems, finite Blaschke products
Subject: Primary: 42A16, 46N99

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.


The author was partially supported by the University of Iowa Department of Mathematics NSF VIGRE grant DMS-0602242.

Author information

Department of Mathematics, University of Iowa, Iowa City, IA 52242