Abstract
In this paper, we use the connection between the classic trigonometric Caratheodory problem and the maximum entropy Burg problem for a stationary processes to obtain from an Operator Theory point of view: Levinson’s algorithm, Schur’s recursions and the Christoffel-Darboux formula. We deal with a functional model due to Arov and Grossman, which provides a complete description of all minimal unitary extensions of an isometry by the Schur class, in order to describe all the solutions of the Covariance Extension Problem and then we obtain the density that solves the maximum entropy problem of Burg.
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Marcano, J., Morán, M. (2005). The Arov-Grossman Model and Burg’s Entropy. In: Baeza-Yates, R., Glaz, J., Gzyl, H., Hüsler, J., Palacios, J.L. (eds) Recent Advances in Applied Probability. Springer, Boston, MA. https://doi.org/10.1007/0-387-23394-6_15
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DOI: https://doi.org/10.1007/0-387-23394-6_15
Publisher Name: Springer, Boston, MA
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