Kutoviy, Oleksandr
Oleksandr
Kutoviy
Analytical methods in constructive measure theory on configuration spaces
Analytische Methoden in konstruktiver Maßtheorie auf Konfigurationsräumen
Bielefeld University
2003
2004-02-27T13:31:30Z
2018-07-24T13:00:09Z
bi_dissertation
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The configuration spaces over an Euclidean space $R^{d}$ which consist of all locally finite subsets of $R^{d}$ are considered.
The present thesis can be characterized as a further development of the constructive part of the infinite dimensional analysis on the configuration spaces. In particular it is related with the investigation of some classes of measures on configuration spaces. Among measures, considered on the configuration spaces, one should distinguish the class of measures constructed via potentials of interaction. These measures are known in mathematical physics as Gibbs measures. The aim of the following dissertation is constructive study of probability measures on configuration spaces, using new analytical methods developed in the present thesis, and application of the obtained results to Gibbs class measures.