Analysis and geometry on marked configuration spaces (Q2751503)

In the introduction the authors mention that in recent years stochastic analysis and differential geometry on configuration space have been developed in a series of papers (see the authors' references). The geometry of the configuration space \(\Gamma_X\) over a Riemannian manifold \(X\) can be realised by a ``lifting procedure'' and is determined by the Riemannian structure of \(X\). In the note by \textit{Yu. G. Kondratiev}, \textit{E. W. Lytvynov} and \textit{G. F. Us} [Methods Funct. Anal. Topol. 5, No. 1, 29-64 (1999; Zbl 0956.58004)] the model case \(M=R_+\) is considered which represents the case of a compound Poisson measure.NEWLINENEWLINENEWLINEIn the present note, the anterior results are generalized to the case where \(M\) is a homogeneous space of a Lie group \(G\). Chapter 1 treates Markov measures. Chapter 2 is devoted to the transformations of the marked Poisson measure. Chapter 3 studies the differential geometry of marked configuration spaces. Chapter 4 contains an information about the representation of Lie algebra. Chapter 5 is entitled ``Intrinsic Dirichlet forms on marked Poisson spaces''. The last chapter describes different considerations about intrinsic Dirichlet operators as a second quantization.NEWLINENEWLINEFor the entire collection see [Zbl 0964.00042].