On some theorems of Hurwitz and Sheil-Small
1986 ◽
Vol 100
(2)
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pp. 365-370
We recall a theorem of Hurwitz [5]: let f(θ) be real-valued and periodic, f(θ) ≢ 0, andwhere 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].
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1944 ◽
Vol 40
(3)
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pp. 253-255
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1992 ◽
Vol 111
(3)
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pp. 599-608
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1950 ◽
Vol 46
(4)
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pp. 549-554
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1952 ◽
Vol 1
(1)
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pp. 13-15
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1975 ◽
Vol 77
(1)
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pp. 159-169
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1978 ◽
Vol 21
(1)
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pp. 11-15
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1950 ◽
Vol 46
(3)
◽
pp. 406-418
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