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2013 | OriginalPaper | Chapter
The Work of Wiener and Masani on Prediction Theory and Harmonic Analysis
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The work of Norbert Wiener and Pesi Masani started at Indian Statistical Institute in Kolkata during the visit of Wiener in 1955–56. Wiener [18] had done substantial work on the prediction problem for univariate (weakly) stationary (henceforth, stationary) processes and had partial results for multivariate stationary processes. A.N. Kolmogorov [7] had studied the univariate case in detail, with emphasis on a fundamental theorem of H. Wold. In addition, V. Zasuhin [20] had announced partial results. Because of the connection between prediction theory (of interest to Wiener) and factorization of matrix-valued functions (of interest to Wiener [18] p.150 and Masani [12]), their collaboration produced results and techniques which had a lasting influence on prediction theory, analysis and operator theory (Nagy and Foias, see [13]).