Symmetries of Gaussian measures and operator colligations

Details Symmetries of Gaussian measures and operator colligations Symmetries of Gaussian measures and operator colligations

2011-11-15

arxiv.org/abs/1111.3474v1

Mathematics

Representation Theory

21pp

Scientific paper

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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