Nonnegative Trigonometric Polynomials
نویسندگان
چکیده
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 explicitly. Associated cosine polynomials kn(θ) are constructed in such a way, that {kn(θ)} are summability kernels. Thus, the Lp, pointwise and almost everywhere convergence of the corresponding convolutions is established.
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تاریخ انتشار 2001