Change search
ReferencesLink to record
Permanent link

Direct link
The moment problem for rational measures: convexity in the spirit of Krein
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. KTH, School of Engineering Sciences (SCI), Centres, Center for Industrial and Applied Mathematics, CIAM. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.ORCID iD: 0000-0002-2681-8383
2009 (English)In: MODERN ANALYSIS AND APPLICATIONS: MARK KREIN CENTENARY CONFERENCE / [ed] Adamyan, V; Berezansky, Y; Gohberg, I; Gorbachuk, M; Gorbachuk, V; Kochubei, A; Langer, H; Popov, G, Birkhäuser Verlag, 2009, Vol. 190, 157-169 p.Conference paper (Refereed)
Abstract [en]

The moment problem as formulated by Krein and Nudel'man is a beautiful generalization of several important classical moment problems, including the power moment problem, the trigonometric moment problem and the moment problem arising in Nevanlinna-Pick interpolation. Motivated by classical applications and examples, in both finite and infinite dimensions, we recently formulated a new version of this problem that we call the moment problem for positive rational measures. The formulation reflects the importance of rational functions in signals, systems and control. While this version of the problem is decidedly nonlinear, the basic tools still rely on convexity. In particular, we present a solution to this problem in terms of a nonlinear convex optimization problem that generalizes the maximum entropy approach used in several classical special cases.

Place, publisher, year, edition, pages
Birkhäuser Verlag, 2009. Vol. 190, 157-169 p.
, Operator Theory Advances and Applications, ISSN 0255-0156 ; 190
Keyword [en]
Moment problems, interpolation, rational positive measures, convex optimization
National Category
URN: urn:nbn:se:kth:diva-60766DOI: 10.1007/978-3-7643-9919-1_9ISI: 000270064800009ISBN: 978-3-7643-9918-4OAI: diva2:477898
International Conference on Modern Analysis and Applications Location: Odessa, UKRAINE Date: APR 09-14, 2007
QC 20120221Available from: 2012-01-14 Created: 2012-01-14 Last updated: 2012-02-21Bibliographically approved

Open Access in DiVA

No full text

Other links

Publisher's full text

Search in DiVA

By author/editor
Lindquist, Anders
By organisation
Optimization and Systems TheoryCenter for Industrial and Applied Mathematics, CIAMACCESS Linnaeus Centre

Search outside of DiVA

GoogleGoogle Scholar
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

Altmetric score

Total: 18 hits
ReferencesLink to record
Permanent link

Direct link