A limit theorem for Szego polynomials with respect to convolution of point masses with the Fejer kernel

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:327

Article

Arciero, Michael

关键词: Szego polynomial;    orthogonal polynomial;    frequency analysis;    Fejer kernel;   

DOI  :  10.1016/j.jmaa.2006.04.025

来源: Elsevier

【 摘 要 】

Two recently-proposed methods for estimating the m frequencies of a trigonometric signal using Szego polynomials of fixed degree k > m consist of multiplying the moments of the n-truncated periodogram by the moments of the Poisson kernel and the wrapped Gaussian, respectively, in an effort to address the nonconvergence of the polynomials as n -> infinity. These methods are seen to be equivalent to convolution of point masses with approximate identities, suggesting a general method. We characterize the limit polynomial for the case when the approximate identity is the Fejer kernel, extending recent results of the author for the case of the Poisson kernel. Moreover, the limit is seen to be the same as in the former case. (c) 2006 Elsevier Inc. All rights reserved.

【 授权许可】

Free