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Existence of smooth solutions to the classical moment problems
Journal article   Open access   Peer reviewed

Existence of smooth solutions to the classical moment problems

Transactions of the American Mathematical Society, Vol.332(2), pp.839-848
1992
DOI: 10.1090/S0002-9947-1992-1059709-1
url
https://doi.org/10.1090/S0002-9947-1992-1059709-1View
Published (Version of record) Open Access

Abstract

Let s(0), s(l), … be a given sequence, and define holds for all finite sequences (ξn n ε z, then it is known that there is a positive Borel measure μ. on the circle T such that sequence (s(n) that the measure μ. may be chosen to be smooth. A measure μ is said to be smooth if it has the same spectral type as the operator id/dt acting on L2(𝕋) with respect to Haarmeasure dt on 𝕋 : Equivalently, μ is a superposition (possibly infinite) of measures of the form ω(i)dt with ωL2(𝕋) such that dw/dt e L2(T). The condition is stated purely in terms of the initially given sequence (s(n)): We show that a smooth representation exists if and only if, for the a priori estimate.

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