On the support of quasi-invariant measures on infinite-dimensional Grassmann manifolds. (English) Zbl 0621.28009
One antisymmetric analogue of Gaussian measure on a Hilbert space is a certain measure on a finite-dimensional Grassmann manifold. The author shows that the characteristic function of this measure is continuous in a weighted norm for graph coordinates. As a consequence the measure is supported on a thickened Grassmann manifold. The action of certain unitary transformations extends to this thickened Grassmannian, and the measure is quasi-invariant with respect to these point transformations.
Reviewer: P.Raboin
MSC:
| 28C20 | Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) |
| 46G12 | Measures and integration on abstract linear spaces |
Keywords:
quasi-invariant measure; support of a measure; Gaussian measure; Hilbert space; characteristic function; thickened Grassmann manifoldReferences:
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