Journal article
Solution of the singular quartic moment problem
Journal of operator theory, Vol.48(2), pp.315-354
09/01/2002
Abstract
In this note we obtain a complete solution to the quartic problem in the case when the associated moment matrix M(2)(gamma) is singular. Each representing measure mu satisfies card supp mu greater than or equal to rank M(2), and we develop concrete necessary and sufficient conditions for the existence and uniqueness of representing measures, particularly minimal ones. We show that rank M(2)-atomic minimal representing measures exist in case the moment problem is subordinate to an ellipse or non-degenerate hyperbola. If the quartic moment problem is subordinate to a pair of intersecting lines, those problems subordinate to a general intersection of two conics may not have any representing measure at all. As an application, we describe the minimal quadrature rules of degree 4 for arclength measure on a parabolic arc.
Details
- Title: Subtitle
- Solution of the singular quartic moment problem
- Creators
- R E CurtoL A Fialkow
- Resource Type
- Journal article
- Publication Details
- Journal of operator theory, Vol.48(2), pp.315-354
- Publisher
- THETA FOUNDATION
- ISSN
- 0379-4024
- eISSN
- 1841-7744
- Number of pages
- 40
- Language
- English
- Date published
- 09/01/2002
- Academic Unit
- Mathematics
- Record Identifier
- 9984240762102771
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