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The Multidimensional Moment Problem with Complexity Constraint
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.ORCID iD: 0000-0001-5158-9255
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. Shanghai Jiao Tong University, China.ORCID iD: 0000-0002-2681-8383
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.ORCID iD: 0000-0002-9778-1426
2016 (English)In: Integral equations and operator theory, ISSN 0378-620X, E-ISSN 1420-8989, Vol. 84, no 3, 395-418 p.Article in journal (Refereed) Published
Abstract [en]

A long series of previous papers have been devoted to the (one-dimensional) moment problem with nonnegative rational measure. The rationality assumption is a complexity constraint motivated by applications where a parameterization of the solution set in terms of a bounded finite number of parameters is required. In this paper we provide a complete solution of the multidimensional moment problem with a complexity constraint also allowing for solutions that require a singular measure added to the rational, absolutely continuous one. Such solutions occur on the boundary of a certain convex cone of solutions. In this paper we provide complete parameterizations of all such solutions. We also provide errata for a previous paper in this journal coauthored by one of the authors of the present paper.

Place, publisher, year, edition, pages
Springer, 2016. Vol. 84, no 3, 395-418 p.
Keyword [en]
complexity constraints, Moment problems, multidimensional moment problems, optimization, smooth parameterization
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-175025DOI: 10.1007/s00020-015-2248-zISI: 000371077100004Scopus ID: 2-s2.0-84959192629OAI: oai:DiVA.org:kth-175025DiVA: diva2:876696
Note

QC 20160323

Available from: 2015-12-04 Created: 2015-10-09 Last updated: 2017-12-01Bibliographically approved

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Karlsson, JohanLindquist, AndersRingh, Axel

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