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.
"Hardy-Type Space Associated with an Infinite-Dimensional Unitary Matrix Group." Abstr. Appl. Anal. 2013 1 - 7, 2013. https://doi.org/10.1155/2013/810735