Norms of positive definite toeplitz matrices and detection of almost periodic components in random signals

For positive definite Toeplitz matrices generated by trigonometric moments of a non-negative measure we note that the Hilbert-Schmidt norm and the maximal eigenvalue satisfy certain limiting relations. Analogous relations hold for positive definite integral operators with difference kernels. The obtained relations are used in order to detect hidden almost periodic components in random signals.The financial support of the Polytechnic University of Valencia is gratefully acknowledged.Adamyan, V.; Iserte Vilar, JL.; Tkachenko Gorski, IM.; Verdú Martín, GJ. (2014). Norms of positive definite toeplitz matrices and detection of almost periodic components in random signals. Operators and Matrices. 8(3):861-875. doi:10.7153/oam-08-488618758