Artigo
Nonnegative trigonometric polynomials
Fecha
2002-12-01Registro en:
Constructive Approximation, v. 18, n. 1, p. 117-143, 2002.
0176-4276
10.1007/s00365-001-0004-x
WOS:000172211500006
2-s2.0-0036103878
Autor
Universidade Estadual Paulista (Unesp)
Resumen
An extremal problem for the coefficients of sine polynomials, which are nonnegative in [0,π] , posed and discussed by Rogosinski and Szego is under consideration. An analog of the Fejér-Riesz representation of nonnegative general trigonometric and cosine polynomials is proved for nonnegative sine polynomials. Various extremal sine polynomials for the problem of Rogosinski and Szego are obtained explicitly. Associated cosine polynomials k n (θ) are constructed in such a way that { k n (θ) } are summability kernels. Thus, the L p , pointwise and almost everywhere convergence of the corresponding convolutions, is established. © 2002 Springer-Verlag New York Inc.