The moment problem for rational measures: convexity in the spirit of Krein
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)
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
Moment problems, interpolation, rational positive measures, convex optimization
IdentifiersURN: urn:nbn:se:kth:diva-60766DOI: 10.1007/978-3-7643-9919-1_9ISI: 000270064800009ISBN: 978-3-7643-9918-4OAI: oai:DiVA.org:kth-60766DiVA: diva2:477898
International Conference on Modern Analysis and Applications Location: Odessa, UKRAINE Date: APR 09-14, 2007
QC 201202212012-01-142012-01-142012-02-21Bibliographically approved