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Generalized Herglotz theorem in vector lattices. (English) Zbl 0893.28008
A Herglotz theorem is presented in the context of vector lattices: A necessary and sufficient condition for a sequence \((y_n)\) of elements of a (Dedekind) complete vector lattice \(Y\) to be positive definite is that there exits a positive measure \(m\) with values in \(Y\) on the Borel sets of the circle group such that \(y_n\) are Fourier-Stieltjes coefficients of \(m\).
MSC:
28B15 Set functions, measures and integrals with values in ordered spaces
42A82 Positive definite functions in one variable harmonic analysis
42A16 Fourier coefficients, Fourier series of functions with special properties, special Fourier series
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References:
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