Journal article
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
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.
Details
- Title: Subtitle
- Existence of smooth solutions to the classical moment problems
- Creators
- Palle E.T. Jorgensen - University of Iowa, Mathematics
- Resource Type
- Journal article
- Publication Details
- Transactions of the American Mathematical Society, Vol.332(2), pp.839-848
- DOI
- 10.1090/S0002-9947-1992-1059709-1
- ISSN
- 0002-9947
- eISSN
- 1088-6850
- Number of pages
- 10
- Language
- English
- Date published
- 1992
- Academic Unit
- Mathematics
- Record Identifier
- 9984241155302771
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