A limit theorem for Szegö polynomials with respect to convolution of point masses with the Fejér kernel

Two recently-proposed methods for estimating the m frequencies of a trigonometric signal using Szegö 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→∞. 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 Fejér 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. © 2006 Elsevier Inc. All rights reserved.