On Nonnegative Cosine Polynomials with Nonnegative Integral Coefficients
نویسندگان
چکیده
We show that there exist Po > 0 ar>d P\, ■■■ , Pn nonnegative integers, such that 0 < p(x) = Po + Pi cosx + • ■ • + Pn cos Nx and po -C s1/3 for .s = J2'J=oPj < improving on a result of Odlyzko who showed the existence of such a polynomial p that satisfies Po < (.slogs)1/3 . Our result implies an improvement of the best known estimate for a problem of Erdos and Szekeres. As our method is nonconstructive, we also give a method for constructing an infinite family of such polynomials, given one good "seed" polynomial.
منابع مشابه
A Modified Digital Image Watermarking Scheme Based on Nonnegative Matrix Factorization
This paper presents a modified digital image watermarking method based on nonnegative matrix factorization. Firstly, host image is factorized to the product of three nonnegative matrices. Then, the centric matrix is transferred to discrete cosine transform domain. Watermark is embedded in low frequency band of this matrix and next, the reverse of the transform is computed. Finally, watermarked ...
متن کاملA Modified Digital Image Watermarking Scheme Based on Nonnegative Matrix Factorization
This paper presents a modified digital image watermarking method based on nonnegative matrix factorization. Firstly, host image is factorized to the product of three nonnegative matrices. Then, the centric matrix is transferred to discrete cosine transform domain. Watermark is embedded in low frequency band of this matrix and next, the reverse of the transform is computed. Finally, watermarked ...
متن کاملNonnegative Trigonometric Polynomials
An extremal problem for the coefficients of sine polynomials, which are nonnegativein [0, π], posed and discussed by Rogosinski and Szegő is under consideration. An analog of the Fejér-Riesz representation of nonnegativegeneral trigonometric and cosine polynomials is proved for nonnegativesine polynomials. Various extremal sine polynomials for the problem of Rogosinski and Szegő are obtained ex...
متن کاملDiscrete Transforms, Semidefinite Programming, and Sum-of-Squares Representations of Nonnegative Polynomials
Abstract. We present a new semidefinite programming formulation of sum-of-squares representations of nonnegative polynomials, cosine polynomials and trigonometric polynomials of one variable. The parametrization is based on discrete transforms (specifically, the discrete Fourier, cosine and polynomial transforms) and has a simple structure that can be exploited by straightforward modifications ...
متن کاملPolynomials with Nonnegative Coefficients
The authors verify the conjecture that a conjugate pair of zeros can be factored from a polynomial with nonnegative coefficients so that the resulting polynomial still has nonnegative coefficients. The conjecture was originally posed by A. Rigler, S. Trimble, and R. Varga arising out of their work on the Beauzamy-Enflo generalization of Jensen's inequality. The conjecture was also made independ...
متن کامل