Second quantisation for skew convolution products of measures in Banach spaces (Q2637755)

In the paper the measures in Banach space are studied, which arise as the skew convolution product of two other measures, where the convolution is deformed by a skew map. It is shown how that given such a set-up the skew map can be lifted to an operator that acts at the level of function spaces and also it is demonstrated that this is an example of the well known functorial procedure of second quantisation. The particular emphasis is given to the case where the product measure is infinitely divisible and the second quantisation process is studied in some detail using chaos expansions when this is either Gaussian or is generated by a Poisson random measure. A key part of the authors approach is the use of a family of vectors that they call exponential martingale vectors