论文信息 - The first sign change of a cosine polynomial

The first sign change of a cosine polynomial

It is reasonable to expect the first sign change of a real cosine polynomial to decrease when its smallest frequency is increased. Many cases in which this is true are exhibited, but it is shown that there exist (presumably unusual) cosine polynomials for which the first sign change may increase by an arbitrarily large amount.

J. Nulton | K. Stolarsky | Kenneth B. Stolarsky | James D. Nulton

[1] K. F. Roth. On cosine polynomials corresponding to sets of integers , 1973 .

[2] P. Stein. On the Real Zeros of a certain Trigonometric Function , 1935, Mathematical Proceedings of the Cambridge Philosophical Society.

[3] J. Littlewood. Some problems in real and complex analysis , 1968 .

[4] D. G. Dickson. Zeros of exponential sums , 1965 .

[5] Mark Kac,et al. On the Distribution of Values of Trigonometric Sums with Linearly Independent Frequencies , 1943 .

[6] J. J. Price. Topics in Orthogonal Functions , 1975 .

[7] A. A. Talalyan. THE REPRESENTATION OF MEASURABLE FUNCTIONS BY SERIES , 1960 .

[8] P. J. Cohen. On a Conjecture of Littlewood and Idempotent Measures , 1960 .