A Herglotz Theorem in Ordered Vector Spaces Which Are Not a Lattice
نویسندگان
چکیده
The classical Herglotz theorem states that a sequence (ak) ∞ k=−∞ of complex numbers is the sequence of the Fourier-Stieltjes coefficients of a non-decreasing function g defined on the interval 〈0, 2π〉 if and only if the sequence (ak)k=−∞ is positive definite. Recall that ak = ∫ 2π 0 e dg(t) is said to be the kth FourierStieltjes coefficient of a function g (with bounded variation defined on the interval 〈0, 2π〉). A sequence (ak)k=−∞ of complex numbers is said to be positive definite if and only if
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