Malliavin Operator Calculus on Countable Products of Heisenberg Matrix Groups

Using the Malliavin-Skorokhod dual relations, the operator calculus on Weyl-Schrödinger representations for countable products of Heisenberg matrix groups with entries in Wiener spaces is developed. Applications to Bernstein-Jackson inequalities for approximations of Skorokhod discrete divergences by decreasing rearrangements of coherent states are presented.