高斯测度的对称性与算子系综
Symmetries of Gaussian measures and operator colligations
摘要：
考虑一个无限维线性空间，该空间具有一个高斯测度和一组$GL(\infty)$，该组线性变换将该测度转换为等价测度。$GL(\infty)$的极限点可以被认为是“扩散”图（多态性）。证明了多态半群中$GL(\infty)$的闭包包含一定的算子系综半群，并给出了算子系综作用于具有高斯测度的空间多态的显式公式.
英文摘要：
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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