Thesis /

ROMDOC-THESIS-2010-108

Probleme de tip Markov şi Sharafutdinov în teoria momentelor

Mihaila, Janina Mihaela (UPB)
2007-01-01

Abstract: This paper is a study on Markov and Sharafutdinov type moment problems. More precisely, it investigates the existence, the uniqueness and the construction of some solution of the moment problems, and at the same time, the adaptation of moment problem solution to submanifolds. The work solves some operator-valued Markov-type moment problems, specifically in spaces of analytic functions of several complex variables on closed polydiscs. The present work emphasizes the relation between the Markov-type moment problems and the differential geometry and it constructs some functions by the prescribed moments. This paper formulates and studies the problem of determination of a metric by its boundary energy in the single-time case, and it extends the problem to the multi-time case. Using the linearization, it extends the problem to the multi-ray transform of a distinguished tensor field and to the moment problem. The final chapter uses a version of the Newton’s method for operators to approximate the solutions of some operatorial equations and to solve some differential equations, with matrix and operator coefficients.

Keyword(s): Procese Markov -- Statistică matematică ; Geometrie diferenţială -- Teză de doctorat ; Analiză funcţională -- Analiză matematică -- Teză de doctorat
Note: Udriste, Constantin

OPAC: See record in BC-UPB Web OPAC
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