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## Banach Center Publications

1997 | 38 | 1 | 75-104
Tytuł artykułu

### An operator-theoretic approach to truncated moment problems

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We survey recent developments in operator theory and moment problems, beginning with the study of quadratic hyponormality for unilateral weighted shifts, its connections with truncated Hamburger, Stieltjes, Hausdorff and Toeplitz moment problems, and the subsequent proof that polynomially hyponormal operators need not be subnormal. We present a general elementary approach to truncated moment problems in one or several real or complex variables, based on matrix positivity and extension. Together with the construction of a "functional calculus" for the columns of the associated moment matrix, our operator-theoretic approach allows us to obtain existence theorems for the truncated complex moment problem, in case the columns satisfy one of several natural constraints. We also include an application to the Riemann-quadrature problem from numerical analysis.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Numer
Strony
75-104
Opis fizyczny
Daty
wydano
1997
Twórcy
autor
• Department of Mathematics, The University of Iowa, Iowa City, Iowa 52242, U.S.A.
Bibliografia
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Bibliografia
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