Functional calculus for countable set of operators over symmetric Fock space

Abstract

In this paper we construct an operator calculus over the symmetric Fock space for countable set of noncommuting generators of strongly continuous groups, acting on a Hilbert space. As a symbol class of the calculus we use some algebra of functions of infinitely many variables. This algebra is described as the image of the space of polynomial ultradifferentiable functions under Fourier-Laplace transformation.