Mierzejewski D. Generalized Jacobi fields and a chaotic representation for the Gamma field

The objects of research are generalized Jacobi fields. The aim of research is to generalize the spectral approach to the white noise analysis and to construct a (generalized) chaotic representation connected with the gamma measure. For this aim methods of functional analysis were used. A generalization of the spectral approach to the white noise analysis, based on a generalization of the notion of Jacobi field, is constructed. It is proved that the gamma field is a generalized Jacobi field. It is proved that n-particle subspace of the extended Fock space can be understood as an orthogonal sum of certain functional spaces. A chaotic representation for the gamma field is constructed. The field of utilization is the white noise analysis.