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- W77444123 abstract "This chapter presents two remarks related to the result due to Kolmogorov that if Γ(m,n) is a nonnegative definite function from N × N to C, then there exists a sequence {x n , n ∈ N} in a Hilbert space H such that Γ(m,n) = (x m , x n ) H . The first remark is a theorem holding for nonnegative definite functions from T × T to C, where T is an arbitrary index set. Applications are given to Hilbert-valued measures. The second remark applies to separable Hausdorff spaces T, continuous nonnegative definite functions Γ from T × T to C, and separable Hilbert spaces H, and it provides a direct construction of a continuous H-valued function x on T. The second remark was suggested to one of the authors by P. Masani." @default.
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- W77444123 date "1973-01-01" @default.
- W77444123 modified "2023-09-26" @default.
- W77444123 title "SOME REMARKS ON A THEOREM OF KOLMOGOROV" @default.
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- W77444123 doi "https://doi.org/10.1016/b978-0-12-702450-9.50006-3" @default.
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