The ordinary Fock space is the Hilbert space of entire functions , with inner product
The present paper studies a generalized Fock space for in which the inner product is
where is a quotient of gamma functions. The authors show that the Dunkl operator
defines a reproducing kernel in such that
Among other results, they show that so that is a subspace of . They study the multiplication operator on defined by and show that , so that and are adjoints of one another. This leads to various results on commutator relations and generalized Weyl relations between and .