Extension of explicit formulas in Poissonian white noise analysis using harmonic analysis on configuration spaces
Kondratiev, Tobias Kuna, Oliveira · Condensed Matter Physics · 2008
Harmonic analysis on configuration spaces is used in order to extend explicit expressions for the images of creation, annihilation, and second quantization operators in L 2 -spaces with respect to Poisson point processes to a set of functions larger than the space obtained by directly using chaos expansion.This permits, in particular, to derive an explicit expression for the generator of the second quantization of a sub-Markovian contraction semigroup on a set of functions which forms a core of the generator.