Hardy-Type Space Associated with an Infinite-Dimensional Unitary Matrix Group
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 compl...
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/810735 |
| Summary: | 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. |
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| ISSN: | 1085-3375 1687-0409 |