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Stationarity of operator algebras. (English) Zbl 0796.46041
Summary: It is shown that stationary random fields on an arbitrary locally compact group are exactly Fourier transforms of orthogonally scattered mappings on the \(C^*\)-algebra of the group. This result is obtained as a consequence of a theorem stating that each orthogonal form on a \(C^*\)- algebra is determined by two functionals on the algebra.

MSC:
46L05 General theory of \(C^*\)-algebras
43A25 Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups
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