Journal article
The quadratic moment problem for the unit circle and unit disk
Integral Equations and Operator Theory, Vol.38(4), pp.377-409
12/2000
DOI: 10.1007/BF01228605
Abstract
For the quadratic complex moment problem $$\gamma _{ij} = \int {\bar z^i } z^j d\mu \left( {0 \leqslant i + j \leqslant 2} \right)$$ , we obtain necessary and sufficient conditions for the existence of representing measures μ supported in the unit circleT or in the closed unit disk $$\bar D$$ . We explicitly construct all finitely atomic representing measures supported inT or $$\bar D$$ which have the fewest atoms possible. For the quadratic $$\bar D$$ -moment problem in which the moment matrixM(1) is positive and invertible, there exists an ellipse εɛD such that the minimal (3-atomic) representing measures are supported in the complement of the interior region of ε. Finally, we apply these results to obtain information on the location of the zeros of certain cubic polynomials.
Details
- Title: Subtitle
- The quadratic moment problem for the unit circle and unit disk
- Creators
- Raúl Curto - Department of Mathematics The University of Iowa 52242 Iowa City Iowa USALawrence Fialkow - Department of Mathematics and Computer Science State University of New York College at New Paltz 12561 New Paltz NY USA
- Resource Type
- Journal article
- Publication Details
- Integral Equations and Operator Theory, Vol.38(4), pp.377-409
- Publisher
- Birkhäuser-Verlag; Basel
- DOI
- 10.1007/BF01228605
- ISSN
- 0378-620X
- eISSN
- 1420-8989
- Language
- English
- Date published
- 12/2000
- Academic Unit
- Mathematics
- Record Identifier
- 9983985816302771
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