Heat Kernel Analysis and Cameron-martin Subgroup for Infinite Dimensional Groups
نویسنده
چکیده
The heat kernel measure μt is constructed on GL(H), the group of invertible operators on a complex Hilbert space H. This measure is determined by an infinite dimensional Lie algebra g and a Hermitian inner product on it. The Cameron-Martin subgroup GCM is defined and its properties are discussed. In particular, there is an isometry from the Lμt -closure of holomorphic polynomials into a space H(GCM ) of functions holomorphic on GCM . This means that any element from this Lμt -closure of holomorphic polynomials has a version holomorphic on GCM . In addition, there is an isometry from H(GCM ) into a Hilbert space associated with the tensor algebra over g. The latter isometry is an infinite dimensional analog of the Taylor expansion. As examples we discuss a complex orthogonal group and a complex symplectic group. Table of
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