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Stieltjes Moment Problems and the Friedrichs Extension of a Positive Definite Operator

✍ Scribed by H.L. Pedersen

Publisher: Elsevier Science
Year: 1995
Tongue: English
Weight: 567 KB
Volume: 83
Category: Article
ISSN: 0021-9045
DOI: 10.1006/jath.1995.1122

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✦ Synopsis

For an indeterminate Stielijes moment sequence the multiplication operator (M p(x)=x p(x)) is positive definite and has self-adjoint extensions. Exactly one of these extensions has the same lower bound as (M). the so-called Friedrichs extension. The spectral measure of this extension gives a certain solution to the moment problem and we identify the corresponding parameter value in the Nevanlinna parametrization of all solutions to the moment problem. In the case where (\sigma) is indeterminate in the sense of Stieltjes, relations between the (Nevanlinna matrices of) entire functions associated with the measures (t^{k} d \sigma(t)) are derived. The growth of these entire functions is also investigated. r 1995 Academic Press. Inc

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