Hardy-Type Space Associated with an Infinite-Dimensional Unitary Matrix Group

Abstract EN

We investigate an orthogonal system of the homogenous Hilbert-Schmidt polynomials with respect to a probability measure which is invariant under the right action of an infinite-dimensional unitary matrix group.

With the help of this system, a corresponding Hardy-type space of square-integrable complex functions is described.

An antilinear isomorphism between the Hardy-type space and an associated symmetric Fock space is established.