Henry J. Landau

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In this paper, we give a new proof of the solution of the rational covari-ance extension problem, an interpolation problem with historical roots in potential theory, and with recent application in speech synthesis, spectral estimation, stochas-tic systems theory, and systems identification. The heart of this problem is to pa-rameterize, in useful systems(More)
Ahstract-A band-limited signal of finite energy can be reconstructed from its samples taken at the Nyquist rate. Moreover, the reconstruction is stable, a feature crucial for implementation: a small error in the sample values generates ollly a correspondingly small error in the resulting signal. The Nyquist sample values are mutually independent, so that(More)
In a recent paper, D. Hajela and P. Seymour proved that for O~-bt~-b~ 1, ~t=(Iog~ 3)/2, b~b] +(1-b0"b~ +(1-ba)~(l-b~)'_~ 1, and drew from this inequality a variety of interesting results in combinatorial geometry. They also conjectured a generalization of the inequality to n variables, which they showed to imply a lower bound on the number of different(More)