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- W2039342279 abstract "A general form for the covariance of a generalized process with orthogonal values is found in the case where the covariance $B$ depends on test functions and their first derivatives. Specifically, if $B(phi ,phi ) = int {{phi ^2}d{mu _0} + int {phi phi âd{mu _1} + int {{phi ^2}d{mu _2} geqslant 0} } } ;{text {for }}phi epsilon mathcal {D}({mathbf {R}})$ and Radon measures ${mu _0},{mu _1},{mu _2}$, then there exist Radon measures ${nu _0},{nu _1},{nu _2}$ such that $B(phi ,phi ) = int {{phi ^2}d{nu _0} + int {phi phi âd{nu _1} + int {phi {â^2}d{nu _2}} } }$ and, moreover, $int {{f^2}d{nu _0} + int {fgd{nu _1} + int {{g^2}d{nu _2} geqslant 0} } }$ for all $f,gepsilon mathcal {D}({mathbf {R}})$." @default.
- W2039342279 created "2016-06-24" @default.
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- W2039342279 date "1975-01-01" @default.
- W2039342279 modified "2023-09-25" @default.
- W2039342279 title "Covariances of generalized processes with orthogonal values" @default.
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- W2039342279 doi "https://doi.org/10.1090/s0002-9939-1975-0405570-0" @default.
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