# An operator-theoretic approach to truncated moment problems

Banach Center Publications (1997)

- Volume: 38, Issue: 1, page 75-104
- ISSN: 0137-6934

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topCurto, Raúl. "An operator-theoretic approach to truncated moment problems." Banach Center Publications 38.1 (1997): 75-104. <http://eudml.org/doc/208650>.

@article{Curto1997,

abstract = {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.},

author = {Curto, Raúl},

journal = {Banach Center Publications},

keywords = {functional calculus; moment problems; quadratic hyponormality; unilateral weighted shifts; polynomially hyponormal operators; matrix positivity; extension; Riemann-quadrature problem},

language = {eng},

number = {1},

pages = {75-104},

title = {An operator-theoretic approach to truncated moment problems},

url = {http://eudml.org/doc/208650},

volume = {38},

year = {1997},

}

TY - JOUR

AU - Curto, Raúl

TI - An operator-theoretic approach to truncated moment problems

JO - Banach Center Publications

PY - 1997

VL - 38

IS - 1

SP - 75

EP - 104

AB - 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.

LA - eng

KW - functional calculus; moment problems; quadratic hyponormality; unilateral weighted shifts; polynomially hyponormal operators; matrix positivity; extension; Riemann-quadrature problem

UR - http://eudml.org/doc/208650

ER -

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