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

Milton Rosenberg

Journal of Multivariate Analysis, 1974, vol. 4, issue 2, 166-209

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

Keywords: closed; linear; operator; Hilbert-Schmidt; operator-valued; measure; square-integrable; isomorphism; theorem; subordination; theorem; operator; representation; isomorphs; of; operators; Bochners; L2; Theorem; multivariate; weakly-stationary; stochastic; processes; prediction (search for similar items in EconPapers)
Date: 1974
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Citations: View citations in EconPapers (2)

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