The thesis studies truncated moment problems and related reconstruction techniques. It transfers the main aspects of Prony's method from finitely-supported measures to the classes of signed or non-negative measures supported on algebraic varieties of any dimension. The Zariski closure of the support of these measures is shown to be determined by finitely many moments and can be computed from the kernel of moment matrices. Moreover, several reconstruction algorithms are developed which are based on the computation of generalized eigenvalues and allow to recover the components of mixtures of such measures.
| Identifer | oai:union.ndltd.org:uni-osnabrueck.de/oai:osnadocs.ub.uni-osnabrueck.de:ds-202205166868 |
| Date | 16 May 2022 |
| Creators | Wageringel, Markus |
| Contributors | Prof. Dr. Stefan Kunis, Prof. Dr. Timo de Wolff |
| Source Sets | Universität Osnabrück |
| Language | English |
| Detected Language | English |
| Type | doc-type:doctoralThesis |
| Format | application/pdf, application/zip |
| Rights | Attribution-NonCommercial-ShareAlike 3.0 Germany, http://creativecommons.org/licenses/by-nc-sa/3.0/de/ |
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