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• W2065250286 abstract "Let p, q be arbitrary parameter sets, and let H be a Hilbert space. We say that x = (xi)iϵq, xi ϵ H, is a bounded operator-forming vector (ϵHFq) if the Gram matrix 〈x, x〉 = [(xi, xj)]iϵq,jϵq is the matrix of a bounded (necessarily ≥ 0) operator on lq2, the Hilbert space of square-summable complex-valued functions on q. Let A be p × q, i.e., let A be a linear operator from lq2 to lp2. Then exists a linear operator Ǎ from (the Banach space) HFq to HFp on D(A) = {x:x ϵ HFq, A〈x, x〉12 is p × q bounded on lq2} such that y = Ǎx satisfies yj ϵ σ(x) = {space spanned by the xi}, 〈y, x〉 = A〈x, x〉 and 〈y, y〉 = A〈x, x〉12(A〈x, x〉12)∗. This is a generalization of our earlier [J. Multivariate Anal. 4 (1974), 166–209; 6 (1976), 538–571] results for the case of a spectral measure concentrated on one point. We apply these tools to investigate q-variate wide-sense Markov processes." @default.
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• W2065250286 date "1978-06-01" @default.
• W2065250286 modified "2023-09-27" @default.
• W2065250286 title "Infinite-variate wide-sense Markov processes and functional analysis for bounded operator-forming vectors" @default.
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• W2065250286 doi "https://doi.org/10.1016/0047-259x(78)90081-7" @default.
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