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Operators as spectral integrals of operator-valued functions from the study of multivariate stationary stochastic processes

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  • Rosenberg, Milton

Abstract

P. Masani and the author have previously answered the question, "When is an operator on a Hilbert space the integral of a complex-valued function with respect to a given spectral (projection-valued) measure?" In this paper answers are given to the question, "When is a linear operator from q to p the integral of a spectral measure?"; here the values of the integrand are linear operators from the square-summable q-tuples of complex numbers to the square-summable p-tuples of complex numbers, and our spectral measure for q is the "inflation" of a spectral measure for . In the course of this paper, we make available tools for handling the spectral analysis of q-variate weakly stationary processes, 1

Suggested Citation

  • Rosenberg, Milton, 1974. "Operators as spectral integrals of operator-valued functions from the study of multivariate stationary stochastic processes," Journal of Multivariate Analysis, Elsevier, vol. 4(2), pages 166-209, June.
    • Handle: RePEc:eee:jmvana:v:4:y:1974:i:2:p:166-209
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    Cited by:

    1. Boudou, A. & Cabral, E.N. & Romain, Y., 2010. "Centered and non-centered principal component analyses in the frequency domain," Statistics & Probability Letters, Elsevier, vol. 80(2), pages 96-103, January.
    2. Boudou, Alain & Romain, Yves, 2010. "On the integral with respect to the tensor product of two random measures," Journal of Multivariate Analysis, Elsevier, vol. 101(2), pages 385-394, February.

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