ID: 1111.3474

Symmetries of Gaussian measures and operator colligations

November 15, 2011

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Yury A. Neretin
Mathematics
Representation Theory
Dynamical Systems
Functional Analysis
Probability

Consider an infinite-dimensional linear space equipped with a Gaussian measure and the group $GL(\infty)$ of linear transformations that send the measure to equivalent one. Limit points of $GL(\infty)$ can be regarded as 'spreading' maps (polymorphisms). We show that the closure of $GL(\infty)$ in the semigroup of polymorphisms contains a certain semigroup of operator colligations and write explicit formulas for action of operator colligations by polymorphisms of the space with Gaussian measure.

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