A COMBINATORIAL IDENTITY AND ITS APPLICATION TO GAUSSIAN MEASURES
Luigi Accardi, Hui-Hsiung Kuo, Aurel I. Stan · 2007
Assuming that a probability measure on Rd has finite moments of any order, its moments are completely determined by two family of operators. The first family is composed of the neutral (preservation) operators. The second family consists of the commutators between the annihilation and creation operators. As a confirmation of this fact, a characterization of the Gaussian probability measures in terms of these two families of operators is given. The proof of this characterization relies on a simple combinatorial identity.