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Dennis Courtney
Unions of arcs from Fourier partial sums view print
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| Published: |
October 20, 2010 |
| Keywords: |
Fourier coefficients, trigonometric moment problems, finite Blaschke products |
| Subject: |
Primary: 42A16, 46N99 |
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Abstract
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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| Acknowledgements
The author was partially supported by the University of Iowa Department of Mathematics NSF VIGRE grant DMS-0602242.
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| Author information
Department of Mathematics, University of Iowa, Iowa City, IA 52242
dennis-courtney@uiowa.edu
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