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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The first sign change of a cosine polynomial


Author: Jiang Zeng
Journal: Proc. Amer. Math. Soc. 111 (1991), 709-716
MSC: Primary 33B10; Secondary 42A05
MathSciNet review: 1000327
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Abstract: Nulton and Stolarsky [1] studied the first (i.e., the least positive) sign change of a real cosine polynomial as a function of its smallest frequency. In the present article we will study this problem further, especially to point out that their fundamental proposition is not correct, and that therefore their principal hypothesis is unreasonable. Moreover, various results of Nulton and Stolarsky are improved or corrected and two open questions set in their paper are solved.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1991-1000327-3
PII: S 0002-9939(1991)1000327-3
Keywords: Cosine polynomial, frequencies, first sign changes, zeros
Article copyright: © Copyright 1991 American Mathematical Society