ANALYTIC CHARACTERIZATION OF GENERALIZED FOCK SPACE OPERATORS AS TWO-VARIABLE ENTIRE FUNCTIONS WITH GROWTH CONDITION

Duality is established for new spaces of entire functions in two infinite dimensional variables with certain growth rates determined by Young functions. These entire functions characterize the symbols of generalized Fock space operators. As an application, a proper space is found for a solution to a normal-ordered white noise differential equation having highly singular coefficients.