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Commutator of two projections in prediction theory

Published online by Cambridge University Press:  17 April 2009

Takahiko Nakazi
Takahiko Nakazi
Affiliation:
Department of Mathematics, Faculty of Science, (General Education), Hokkaido University, Sapporo 060, Japan.
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Abstract

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Let w be a nonnegative weight function in L1 = L1 (dθ/2π). Let Q and P denote the orthogonal projections to the closed linear spans in L2(wdθ/2π) of {einθ: n ≤ 0} and {einθ: n > 0}, respectively. The commutator of Q and P is studied. This has applications for prediction problems when such a weight arises as the spectral density of a discrete weakly stationary Gaussian stochastic process.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 34 , Issue 1 , August 1986 , pp. 65 - 71
Copyright
Copyright © Australian Mathematical Society 1986

References

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