Analytical functionals and application to Poissonian and harmonic analysis

Abstract

In this paper, we give a construction of test functions space and the corresponding generalized functions space on the Lebesgue–Poisson space . We use the characterization theorem of the space and the properties of the K-transform to study combinatorial harmonic analysis on configuration space. In particular, using the S _λ-transform we characterize the Bogoliubov functional in terms of certain analytical and growth condition properties.

Keywords:

• Poisson measure
• chaos decomposition
• configuration spaces
• correlation function
• space of analytical functions with growth condition of θ-exponential type
• Bogoliubov functionals

AMS Subject Classification:

• primary 28C20
• secondary 46F25
• 46G20
• 82B21

Notes

^1. [email protected]

Additional information

Notes on contributors

Habib Ouerdiane

1. 1. [email protected]