Unions of arcs from Fourier partial sums

Details Unions of arcs from Fourier partial sums Unions of arcs from Fourier partial sums

2010-02-03

arxiv.org/abs/1002.0639v2

New York J. Math. 16 (2010) 235-243

Mathematics

Functional Analysis

7 pages; added reference and minor modification of introduction

Scientific paper

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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