Abstract
We exploit an analogy between the trigonometric moment problem and prediction theory for a stationary stochastic process. Extending this theory, we show how to use correlations between two processes to predict one from the other. In turn, this gives rise to a simple and unified treatment of the Caratheodory and Nehari moment problems.
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Dym, H., and Gohberg, I. (1986). A maximum entropy principle for contractive interpolants.J. Funct. Anal. 65, 83–125.
Ellis, R. L., and Gohberg, I. (1992). Orthogonal systems related to infinite Hankel matrices.J. Funct. Anal. 109, 155–198.
Gohberg, I., and Feldman, I. A. (1974). Convolution equations and projection methods for their solution.Transl. Math. Monographs 41. American Mathematical Society, Providence, RI.
Gohberg, I., and Landau, H. J. (1995). Prediction and the inverse of Toeplitz matrices.Approximation and Compuration (R. Zahar, ed.).Internat. Ser. Numer. Math. 119, 219–230. Birkhaüser, Boston, MA.
Hoffman, K. (1962).Banach spaces of analytic functions. Prentice-Hall, Englewood Cliffs, NJ.
Jaynes, E. T. (1982). On the rationale of maximum entropy methods.Proc. IEEE 70, 939–952.
Landau, H. J. (1987). Maximum entropy and the moment problem.Bull. Amer. Math. Soc. (N.S.) 16, 47–77.
Nehari, Z. (1957). On bounded bilinear forms.Ann. of Math. (2)65, 153–162.
Sarason, D. (1987). Moment problems and operators in Hilbert space.Moments in Mathematics (H. J. Landau, ed.).Proc. Sympos. Appl. Math. 37, 54–70. American Mathematical Society, Providence, RI.
Szegö, G. (1975). Orthogonal polynomials.Amer. Math. Soc. Colloq. Publ. 23. Amer. Math. Soc., Providence, RI.
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Gohberg, I., Landau, H.J. Prediction for two processes and the nehari problem. The Journal of Fourier Analysis and Applications 3, 43–62 (1997). https://doi.org/10.1007/BF02647946
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DOI: https://doi.org/10.1007/BF02647946