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Maximum entropy and the moment problem. (English) Zbl 0617.42004
This paper connects the trigonometric moment problem with some questions centering on prediction and entropy. In turn, this suggests a simple approach, by way of orthogonal decomposition, to the moment problem itself, to associated factorizations of Toeplitz matrices, and, in a continuous version, to certain results of M. G. Krein concerning Sturm- Liouville differential equations.

MSC:
42A70 Trigonometric moment problems in one variable harmonic analysis
42A05 Trigonometric polynomials, inequalities, extremal problems
62M15 Inference from stochastic processes and spectral analysis
94A17 Measures of information, entropy
60G25 Prediction theory (aspects of stochastic processes)
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