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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.
AMS Subject Classification:
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