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On some theorems of Hurwitz and Sheil-Small

Published online by Cambridge University Press:  24 October 2008

R. R. Hall
R. R. Hall
Affiliation:
Department of Mathematics, University of York, York YO1 5DD
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Extract

We recall a theorem of Hurwitz [5]: let f(θ) be real-valued and periodic, f(θ) ≢ 0, and

where an = bn = 0, 0 ≤ n < N. Then f(θ) has at least 2N sign changes in each period. A similar result with a trigonometric polynomial on the right-hand side of (1) had been obtained earlier by Sturm [7].

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 100 , Issue 2 , September 1986 , pp. 365 - 370
Copyright
Copyright © Cambridge Philosophical Society 1986

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References

REFERENCES

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